^^
5^
i
> j^
^^#
*/i
•^^S'
» >
• > ) :
) -3 ~ • •'
i*
*t
^m
>/ » >3
^^ ^
THE
LONDON, EDINBURGH, and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
CONDUCTED BY
SIR DAVID BREWSTER, K.H. LL.D. F.R.S.L. & E. &c.
SIR ROBERT KANE, M.D., F.R.S., M.R.I.A.
WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S.
JOHN TYNDALL, F.R.S. &c.
" Nee aranearum saue textus ideo melior qiiia ex se fila gignunt, nee noster
vilior quia ex alienis libamus ut apes." Just. Lips. Polit. lib. i. cap. 1. Not.
VOL. XIX.— FOURTH SERIES.
JANUARY— JUNE, 1860.
LONDON.
TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Printers and Publishers to the University of London ;
SOLD BY LONGMAN, GREEN, LONGMANS, AND ROBERTS; SIMPKIN', MARSHALL
AND CO.; WHITTAKER AND CO.; .-VND PIPER AND CO., LONDON :
BY ADAM AND CHARLES BLACK, AND THO.MAS CLARK,
EDINBURGH; SMITH AND SON, GLASGOW ; HODGES
AND SMITH, DUBLIN ; AND PUTNAM,
NEW YORK.
'' Meditationis est peiscnitari occulta ; contemplationis est admirari
perspiciia Admii-atio generat qusestionem, qua;stio investigationem,
investigatio inventionem." — Hugo de S. Victore.
— " Cur Spirent venti, cur terra dehiscat.
Cur mare turgescat, pelago cur tantus amaror,
Cur caput obscura Phoebus ferrugine condat,
Quid toties diros cogat llagrare cometas ;
Quid pariat nubes, veniant cur fulmiua ccelo.
Quo micet igne Iris, superos quis conciat orbes
Tam vario motu."
J. B. Pinelli ad Mazonium.
QC
?i*
CONTENTS OF VOL. XIX.
(FOURTH SERIES.)
NUMBER CXXIV.— JANUARY 1860.
Page
Mr. T. Tate on the Construction of certain new forms of
Thermo-Barometers 1
M. W, G. Hankel on the Electric Deportment of the Flame of
Alcohol 9
Mr. R. P. Greg on several New British Minerals 13
Mr. J. N. Hearder's Extracts from Notes on Electrical Conduc-
tivity 14
Prof. Maxwell on the Motions and Collisions of Perfectly Elastic
Spheres 19
Prof. H. Rose on the different States of Silicic Acid 32
Dr. Woods's Description of a new Actinometer 39
Prof. Challis on the possibility of finding a Root, real or imagi-
nary', of every Equation 46
Dr. Atkinson's Chemical Notices from Foreign Journals .... 48
Proceedings of the Royal Society : —
Dr. Pavy on Lesions of the Nervous System producing
Diabetes 52
Dr. Davy on the Electrical Condition of the Egg of the
Common Fowl 55
Mr. J. Toynbee on the transmission of Sonorous Undula-
tions in the Human Ear 56
Mr. J. P. Gassiot on the Electrical Discharge in vacuo with
an extended Series of the Voltaic Battery 59
Dr. Tyndall on the transmission of Radiant Heat through
Gaseous Bodies 60
Messrs. Bunsen andRoscoe's Photochemical Researches. . 61
Dr. Simpson on the Action of Acids on Glycol 69
Proceedings of the Geological Society : —
Mr. T. W. Atkinson on some Bronze Relics from an Auri-
ferous Sand in Siberia 75
Mr. C. Heaphy on the Volcanic Country of Auckland, New
Zealand 75
Mr. T. Burr on the Geology of a part of South Australia. 76
The Rev. J. E. Woods on some Tertiary Deposits in South
Australia 77
On a New Mineral containing Niobium, by Dr. Julius Potyka. 78
IV CONTENTS OF VOL. XIX. FOURTrf SERIES.
Page
On the Pseudo-diascope, by F. O. Ward 79
On the occurrence of Urea in the Organs of the Plagiosto-
mous Fishes, by G. Stiideler 79
NUMBER CXXV.— FEBRUARY.
Prof. Helmholtz on Vowel Sounds 81
Prof. Challis on a Theory of Molecular Forces 88
Prof. Cavalleri on a New Seismometer constructed in the Col-
lege at Monza. (With a Plate.) 102
Dr. Atkinson's Chemical Notices from Foreign Journals .... 116
Prof. Knoblauch on the Interference of Heat 126
Dr. Wright on the Behaviour of Mercury as an Electrode .... 129
Prof. LeConte on the Correlation of Physical, Chemical, and
Vital Force, and the Conservation of Force in Vital Phse-
nomena 133
Notices respecting New Books : —
Mr. S. H. Winter's Elementary Geometrical Drawing . , 148
Proceedings of the Royal Society : —
Sir J. F. W. Herschel on Colour- Blindness 148
Proceedings of the Geological Society : —
Prof. Owen on some Remains ofPoZyp/ycAorfow from Dorking. 158
Mr. S. Allport on some Fossils from near Bahia, South
America 158
Dr. Dawson on some Fossils from the Coal-formation of
Nova Scotia 159
The Rev. P. B. Brodie on the Occurrence of Footsteps of
Chirotherium in the Upper Keuper of Warwickshire . . 1 60
Prof. Goeppert on the Flora of the Silurian, Devonian,
and Lower Carboniferous Formations 160
Captain Spratt on the Freshwater Deposits of Bessarabia,
Aloldavia, Wallachia, and Bulgaria , 1 60
Messrs. T. R. Jones and W. K. Parker on the Recent and
Fossil Foraminifera of the Mediterranean Area 161
Optical Lecture Experiments, by Prof. Knoblauch 162
On the Fixation of the Magnetic Image, by M. J. Nickles . . 164
NUMBER CXXVL— MARCH.
Mr. M. Ponton on certain Laws of Chromatic Dispersion .... 165
Prof. Davy on a Simple and Expeditious Method of estimating
Phosphoric Acid and its Compounds, which is particularly
applicable to the Analysis of Phosphatic Manures and the
A.shes of Plants 181
CONTENTS OF VOL. XIX. — FOURTH SERIES. V
Page
Mr. J. Spiller on the Composition of the Photographic Image. . 186
M. Foucault and Prof. Kirchhoff on the Simultaneous Emission
and Absorption of Rays of the same definite Refrangibility . . 193
Mr. J. Cockle on the Theory of Equations of the Fifth
Degree {concluded) 197
M. J. Jamin on the Equilibrium and Motion of Liquids in Porous
Bodies 204
Dr. Atkinson's Chemical Notices from Foreign Journals 207
Prof. Dufour's Instructions for the better observation of the
Scintillation of the Stars 216
Proceedings of the Royal Society : —
Mr. A. J. Ellis on the Laws of Operation, and the System-
atization of IVlathematics 224
Dr. Hofmann on New Derivatives of Phenylamine and
Ethylamine 232
Proceedings of the Geological Society : —
Prof. J. Phillips on some Sections of the Strata near Oxford 235
Prof. Harkness on the Old Red Sandstone and the Meta-
morphicRocks on the Southern Margin of the Grampians 236
Mr. A. Geikie on the Old Red Sandstone of the South of
Scotland 237
Proceedings of the Royal Institution : —
Prof. Tyndall on the Influence of Magnetic Force on the
Electric Discharge 238
On the Correlation of Physical, Chemical, and Vital Force,
by James Hinton, Esq 243
On the Conductibility of certain Alloys for Heat and Electricity,
by G. Wiedemann 243
NUMBER CXXVII.— APRIL.
M. H. Fizeau on the Effect of the Motion of a Body upon the
Velocity with which it is traversed by Light 245
Mr. T. Tate on a new Instrument for the Mechanical Trisec-
tion of an Angle ; and on the Multisection of an Angle. . . . 261
Mr. M. Ponton on certain Laws of Chromatic Dispersion {con-
tinued) 263
Mr. G. B. Jerrard's Remarks on Mr. Harley's paper onQuintics. 272
Archdeacon Pratt : Is the Problem, " ttow far is the mass of
the earth solid and how far fluid?" excluded from the domain
of positive Science ? 274
Dr. Atkinson's Chemical Notices from Foreign Journals .... 277
Mr. R. P. Greg on Luminosity of Meteors from Solar Reflexion. 287
Mr. R. V. Tuson on a Carbonate of Lead from Leaden Coffins. 291
Prof. Mallett on Osmlou.'i Acid, and the position of Osmium in
the list of Elements 293
VI CONTENTS OF VOL. XIX. — FOURTH SERIES.
Page
Proceedings of the Royal Society : —
Dr. Hofmann on Phosphammonium Compounds 306
Messrs. A. Geuther and R. Cartmell on the Behaviour of
the Aldehydes with Acids 309
Dr. Babington on Spontaneous Evaporation 314
Proceedings of the Geological Society : —
Mr. L. Barrett on some Cretaceous Rocks in Jamaica. ... 318
Mr. R. Godwin-Austen on the Occurrence of a mass of
Coal in the Chalk of Kent, and on some Fossils from
the Grey Chalk near Guildford 318
Mr. S. V.Wood on the Probable Events which succeeded
the Close of the Cretaceous Period 319
Proceedings of the Royal Institution : —
Dr. Faraday on Lighthouse Illumination — the ElectricLight. 320
On Boracic Acid in the Sea- water on the Coast of California, by
Dr. Veatch 323
On a new kind of Sound-figures formed by Drops of a Liquid,
by F. Melde 324
NUMBER CXXVIII.— MAY.
Prof. Miller's Crystallographic Notices 325
Mr. F. A. Abel on the Composition of Water obtained from the
Coal-strata, Bradford Moor, Yorkshire 330
Mr. J. Cockle's Note on the Remarks of Mr. Jerrard 331
Mr. W. K. Sullivan on some Prismatic Forms of Calcite from
Luganure, County of Wicklow 333
Mr. J. J. Waterston on certain Inductions with respect to the
Heat engendered by the possible Fall of a Meteor into the
Sun ; and on a mode of deducing the absolute Temperature
of the Solar Surface from Therraometric Observation 338
Prof. Jellett's Remarks on the Controversy between Arch-
deacon Pratt and Professor Haughton 343
Mr. W. S. B. Woolhouse on the Deposit of Submarine Cables. 345
Mr. M. Ponton on certain Laws of Chromatic Dispersion (con-
cluded) 364
Dr. Atkinson's Chemical Notices from Foreign Journals .... 380
Proceedings of the Royal ^ciety : —
Prof. J. Thomson on Recent Theories and Experiments
regarding Ice at or near its Melting-point 391
Prof. Donkin on the Analytical Theory of the Attraction
of Solids bounded by Surfaces of a Class including the
Ellipsoid 397
Proceedings of the Geological Society : —
Mr. T. Codrington on the probable Glacial Origin of some
Norwegian Lakes 399
CONTENTS OF VOL. XIX. FOURTH SERIES. VU
Page
Mr. T. F. Jamieson on the Drift and Gravels of the North
of Scotland 399
Dr. T. Wright on the Lower Lias of the South of England. 400
]Mr. J. W. Kirkby on the Occurrence of Lingula Credneri
in the Coal-measures of Durham 401
Mr. C. H. G. Thost on the Rocks, Ores, and other Mine-
rals on the property of the ]\Iarquis of Breadalbane . . 402
Note on the Specific Gravity of Electro-deposited Amorphous
Antimony, by G. Gore, Esq 403
On the Production of Ozone by means of a Platinum Wire made
Incandescent by an Electric Current, by AL Le Roux .... 403
Observations on the Use of Insoluble Compounds in Voltaic Piles,
by M. Becquerel ' 404
NUMBER CXXIX.— JUNE.
Prof. J. P. Cooke : Crystalline Form not necessarily an indica-
tion of definite Chemical Composition ; or, on the possible
'\'^ariation of Constitution in a mineral Species independent of
the Phccnomena of Isomorphism 405
Dr. Lamont on Phaenomena observed during Total Eclipses of
the Sun. (With a Plate.) 416
Prof. Hennessy on the Vertical Currents of the Atmosphere . . 421
M. Poinsot on the Percussion of Bodies (continued) 430
Prof. Clausius on the Dynamical Theory of Gases 434
Mr. M. Ponton on the Law of the Wave-lengths corresponding
to certain points in the Solar Spectrum 437
The Rev. S. Haughton on the Thickness of the Crust of the
Earth 444
ITie Rev. S. Earnshaw on a new Theoretical Determination of
the Velocity of Sound 449
M. G. Quincke on a new kind of Electric Current 455
Proceedings of the Royal Society : —
Dr. Dobell on the Infl«ence of White Light on the Growth
and Nutrition of Animals 458
Mr. W. J. M. Rankine on the Thermodynamic Theory of
Steam-engines with dry Saturated Steam 460
Dr. Hofmann on Triphosphonium Compounds 460
Prof. Powell : Comparison of some recently determined
Refractive Indices with Theory 463
Proceedings of the Geological Society : —
Mr. J. Lamont's Notes about Spitzbergen in 1859 467
Mr. C. Moore on the so-called Wealden Beds at Linksfield. 468
New Secondary Pile of great power, by M. G. Plante 468
Note on the Use of Sulphate of Lead in A'oltaic Couples, by M.
Becquerel 469
Index 471
PLATES.
I. Illustrative of Prof. Cavalleri's Description of a New Seismometer.
II. Illustrative of Dr. Lament's Paper on Phsenoraena observed during
Total Eclipses of the Sun.
THE
LONDON, EDINBURGH amd DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
JANUARY 1860.
I. On the Construction of certain new forms of Thermo -Barome-
ters. By T. Tate, Esq.*
THESE instruments are highly useful on account of being
more sensitive than the mercurial barometers. The
thermo-barometer now commonly used is called a Sympieso-
meter by the instrument makers ; it consists of an upright tube
having a globe at the top bent downwards, and a cup at the
lower extremity bent upwards ; the globe is filled with hydrogen
gas ; and a liquid, usually strong sulphuric acid, stands in the
tube and cup. The variations of the pressure of the atmosphere
are indicated by the elevation of the liquid in the tube, a cor-
rection being made for the change of temperature. For this
purpose there are two scales, one moveable, called the barome-
trical scale, the other fixed, called the thermometrical scale ;
the latter is graduated into degrees of temperature, and the
former into equal divisions representing inches and tenths of a
mercurial column. Now the construction of this instrument
is not correct in principle ; for it is constructed on the assump-
tion that the variations of atmospheric pressure are in pro-
portion to the changes in the height of the column of liquid.
The globe is bent downwards to facilitate the graduation of the
thermometrical scale, which is used for giving the correction
for tenjperature : the globe being plunged into a water-bath,
brought to different degrees of heat, corresponding marks are
then made on the scale on a level with the liquid in the tube.
Now it will be observed that, in this process, the gas occupying
the tube is not brought to the temperature of the water-bath ;
whereas to have a correct scale of temperature, the whole volume
of gas, as well as the column of liquid, should be equally heated ;
* Communicated bv the Author.
Phil. Mag. S. 4. Vol. 19. No. 124. Jan. 1860. 13
2 Mr. T. Tate on the Construction of
but to effect this with a sufficient degree of precision, in such a
position of the globe, would not only involve considerable prac-
tical difficulties, but would also require the aid of a catheto-
meter. This constitutes a serious defect in the instrument, for
the points in this scale should be determined with the greatest
possible precision.
In order to avoid these difficulties and sources of error, I have
constructed a simple instrument of this kind in the followmg
manner : —
The instrument consists of a glass tube, A B, in- ^^
serted in a light half-pint flask A, the connexion at
e V being made air-tight ; a thermometrical scale mn ^
attached to the tube ; a moveable barometrical scale
C D ; Q a piece of very thin india-rubber tied over
the top of the tube A B, to keep the external air from
coming in contact with the strong sulphuric acid
occupying a portion of the tube and flask. The
tube A B is about 24 inches long, and about fths
of an inch internal diameter; it is secured to the
flask in the following manner : — Two perforated
corks, e and v, fitting the neck of the flask, are
placed on the tube ; the lower one, e, is coated with
a solution of india-rubber to render it impervious to
air ; the upper cork, v, being raised a little, the cork
e with the tube is pressed down to its proper depth ;
some pieces of chemical cement, fusible at a gentle /
heat, are now placed above the cork e, and a gentle :
heat is applied until the cement melts ; the upper
cork V is then brought down to its place upon the melted cement ;
when the cement has cooled, the tube will be found fr7nhj fixed
in the flask and perfectly air-tight. Strong sulphuric acid of
commerce is introduced through the tube by means of a pipette,
the tube being held in an inclined position.
N.B. All this process of cementing may be obviated by having
a globe and tube bent in the manner shown in the succeeding
diagram ; but I preferred showing how the instrument may be
constructed cheaply, and with materials which may be readily
obtained.
To form the scale ?n n, a narrow strip of paper, about 10 inches
long, may be attached to the middle portion of the tube by means
of a cement of liquid glue. The scale D C may be formed of a
tbin lath covered with paper, about 10 inches in length ; it may
be simply applied by the hand, or it may be made to slide against
an upright board placed at the back of the tube. These scales
are graduated in the following manner : —
The scale mn must be graduated at a time when the weather
certain new forms of Thermo- Barometers. 3
is settled, and when the mercury in the barometer indicates mean
pressure, or nearly mean pressure, that is, about {p), or 29'5
inches. The liquid must be made to stand about the middle of
the stem at mean temperature (/), or 62°. The flask is then
placed in a water-bath, which is brought to different degrees of
temperature (^i), say to 42^, 62°, and 82°, and marks are made
on the paper m n coincident with the level of the liquid in the
stem at these diflferent temperatures ; the spaces between these
marks are respectively divided into twenty equal parts, thereby
forming intervals of 1 degree. These divisions may be extended,
if desirable, as the intervals are very nearly uniform (see for-
mula 6).
The lower part of the barometrical scale D C must be gra-
duated at a time when the weather is settled, and when the mer-
cury in the barometer stands at a high column {p<^, the tempe-
rature of the air being (/) at, or not far from, the mean tempe-
rature. Having placed a mark {p) about the middle of the
scale D C, bring this mark coincident with the temperature t on
the scale m n, and make a mark on D C coincident with the level
of the liquid in the tube ; then the space, — q^, between these
two marks will indicate a change of atmospheric pressure mea-
sured by the column of mercury equal to p — p^. Substitute the
values — 5-2 and 7J—j92>tlius obtained, in equation (4), and deter-
V
mme the value of the constant — , the values of s and h having
been previously found by experiment and observation. Substi-
V
tute the value of — , thus determined, in equation (5), and calcu-
late the values of q^ for p^=i^O, 30-5, and 31 ; these values of
§'2 being marked off from the middle point p on the scale D C,
will give the points corresponding to these pressures; these
spaces may then be subdivided into equal parts so as to read off
tenths and hundredths. In precisely the same manner the
upper part of the scale must be graduated, when the mercury in
the barometer stands at a low column.
The observations of atmospheric pressure are made as fol-
lows : — The temperature of a delicate thermometer being first
noted, the middle point p of the barometrical scale D C is
moved until it coincides with this temperature as marked on the
thermometrical scale m n ; then the mark on the scale D C coin-
cident with the level of the liquid in the tube, will give the atmo-
spheric pressure as measured by a column of mercury.
Constructed in this manner, the errors of the indications can-
Jiot exceed '03 of an inch of a column of mercury. Thus, by any
person possessing ordinary skill in manipulation, an instrument
may be made for a few shillings, which will bo quite ns accurate
B2
4 Mr. T. Tate on the Construction of
in its indications as an ordinary barometer costing about thirty-
shillings, and certainly much more sensitive.
Let p = the pressure of the atmosphere when the gradations
for temperature are made ; h = the height of the column of
liquid in the tube above the level of liquid in the flask, cor-
responding to t temperature, V volume and P pressure of the
gas in the flask, p being constant ; q-^ = the change of the height
of the column at /, temperature, Vj volume and Pj pressure,
p being constant ; q^ = the change of the height of the column
(estimated from the last) at t^ temperature, Y^ volume and Pg
pressure, and p^ atmospheric pressure ; a = the section of the
tube ; b = the section of the liquid in the flask ; s = the specific
gravity of mercury, that of the liquid being unity; — then as-
suming the section of the tube to be uniform, we find
P V — P V •
^^^ V,=V + «9i; Y, = Y + a{q, + q,); ?=p+ --,
hence we get
1 h-a
P-P<i = 1^^--
, b — a
sp + h + q,-^
When b is very large as compared with a, we may take —j— = 1,
and then 1 { sp + h + q, ^1 .,,
P-P2 = 92X-Att +lh .... (2)
where the signs of g-j and q.2 are + when measured upwards,
and — when measured downwards.
This formula expresses the change of atmospheric pressure in
terms of the variables q^ and q^. It is obvious that jo—j^g is not
exactly in the ratio of q^, although it is so very nearly ; for the
value of the quantity within the brackets is but slightly affiected
by any possible values which may be given to the variables q-^
and q^.
Neglecting q^ and //g within the brackets, we obtain the ap-
proximate formula
s{p-Pi)-
^2= y (3)
sp-^h-{- -
^ a
certain new fonns of Thermo-Barometers. 5
Supposing /J —7?2 and q^ to be determmed by observation, q^
being neglected, or t^ = t, the constant —may be found from (2),
viz.
a ^2 s{p-pci)-q^
Again, solving equation (2) for the value of q^, we get
92=^h\\/Mp-P^)^ + {^^ + ^+ -) -(¥2 + ^ + -)|, (5)
which is the formula I have employed for graduating the baro-
metrical scale by giving different values to pci-
By a similar mode of investigation we find^ neglecting the
pressure of the vapour of the liquid,
Here it will be observed that q^ is very nearly in the ratio of
ii — t, that is to say, the graduations on the thermometrical
scale mn are very nearly uniform. Neglecting q^ within the
brackets, and solving the equality for </„ we find
^ (^-0(^i? + A) ... (7)
{t + 4>5H)^{sp-{-h)y+iy
This formula enables us to determine approximately the range
of the thermometrical scale, having given the capacity of the
flask, &c. ; thus let
V=m' *=7'-5,iJ = 29-5, ^=12, ^=62^ /, = 92°,
then we find 5-1 = 5 "8 ; again, for t^ = 32°, the other quantities
being as before, we find ^1= — 5*8; therefore the range =11-6
inches.
In like manner formula (3) enables us to determine approxi-
mately the range of the barometrical scale, having given the
range of the mercurial barometer; thus let 7)2 = '^1 for the lower
part of the scale, and p^=:2S for the upper part, the other quan-
tities being as before, then we find the entire range = 10 inches
nearly. Hence the length of the tube should not be less tiian
21 "6 inches. The range of this instrument, indicating atmo-
spheric change of pressure, is about three times that of the
common barometer.
The instrument which I shall now describe has a range of 7^
times that of the common barometer, and is at the same time
strictly mathematical as regards the principle of construction,
6
Mr. T, Tate on the Construction of
and therefore free from those errors which necessarily arise from
an empirical principle of construction, such as that adopted in
the construction of the foregoing instrument. I have used this
new instrument for some time, and find that its indications
closely agree with those of the common barometer, excepting
when the atmosphere is in an unsettled state, and then the want
of agreement is clearly due to the resistances or sluggishness of
the mercurial column.
This instrument consists of a glass globe A and tube ASP,
containing a portion of strong
sulphuric acid, bent at S to
an angle of about 45° ; M N
a stout scantling of hard wood
fixed in a level position, having
a slit in it extending nearly
from end to end, to allow the
lower portion of the tube to
slide through it, and having
a circular groove extending
from E to N, in which the
globe A slides ; T V a thin
board placed at the back of
M N ; 0 a round pin on a
level with the centre A of the
globe (this pin may be placed
higher if necessary) upon
which the tube S P slides ; er a, scale of temperature attached
to the tube S P ; E G K a sliding square, the stock E G sliding
in a groove formed in the scantling from M to F ; mn the ther-
niometrical scale, which is transferred from the scale e r in a way
hereafter described ; D C the barometrical scale, sliding on the
blade G K, and graduated into equal parts so as to read off" the
height of the mercury column balancing the pressure of the
atmosphere ; Q a piece of thin india-rubber tied over the top of
the tube to keep the external air from coming into contact with
the sulphuric acid.
The observations of atmospheric pressure are made in the fol-
lowing manner : — The temperature, as indicated by a delicate
thermometer, being first noted, the globe A is shifted along the
groove F N until the liquid in the tube stands at this tempera-
ture, as indicated on the scale e r ; the barometrical scale D C is
then shifted until its middle point jo coincides with the same
point of temperature indicated upon the scale m n, and then the
point on the scale D C coincident with the level of the liquid in
the tube will give the pressure of the atmosphere as measured
by a column of mercury.
ce7'tain new forms of Thermo-Barometers. 7
The scales are graduated as follows : — The scale <? r is formed
in exactly the same way as the thermometrical scale of the in-
strument before described, — with this difference, that the gra-
duations in this case are made when the tube S P is placed at an
angle of 45° to the horizon. The globe being placed in the
frame with its tube inclined at an angle of 45°, these marks of
temperature are transferred to the blade G K of the sliding
square and numbered accordingly, thus forming the thermome-
trical scale m n. The specific gravity of mercury being taken at
7*5 times that of the sulphuric acid, a unit of 7'5 inches is taken
on each side of the central point p of the sliding scale D C,
and divided into 100 equal parts ; then each of those parts,
or -075 of an inch, will read '01 of an inch of mercury ; and if
29*5 be the mean pressure at which the scale er is made, the
point j9 will be numbered 29'5; and the point coinciding with
fifty of these divisions below the point p will correspond to 30
inches of mercury, and so on.
The indications of this instrument are independent of the
volume of the globe, as well as of the section of the tube : the
V
ratio — only affects the range of the scales of temperature e r
and m n, which are determined by direct experiment. The su-
periority of this instrument in point of accuracy over the one
previously described, depends on this circumstance, as well as
upon the great extent of its range.
It will be readily seen that the level of the liquid in the globe
is not at all affected by any change of position. The adjust-
ments for any pressure and temperature of the air being made,
it is obvious that the gas in the globe, having the same volume,
must also have the same pressure that it had at the same tempe-
rature when the tube was in its normal position ; hence it follows
that the difference in the vertical column of liquid must exactly
indicate the change that has taken place in the pressure of the
atmosphere. Thus let h■^^ be the vertical column of liquid at /,
temperature, and Pj pressure of gas in the globe when the tube
was in its normal position, that is, when the atmospheric pres-
sure was p ; and let he, be the vertical column at the same tem-
perature /j when the pressure of the atmosphere is ^g ■> then, as
the elastic force of the gas is the same in both cases, we have
;?+ — = Pi, and alsoj92+ -^=Pi>
that is, the difference of atmospheric pressure is exactly propor-
tional to the difference between the vertical columns.
8 On the Construction of new forms of Thermo-Barometers.
Agaiu, let /: = SP, the column of liquid in the tube at a given
temperature t; e = SA; ^=^EOQ, the inclination of the tube
SP ; h ■= the pei-pendicular column of liquid above the level of
the liquid in the globe ; 6^ = any other inclination of the tube
corresponding to ^j perpendicular column, the temperature being
constant ; c = the distance of the level of the liquid in the globe
from its centre ; 7- = OP ; — then we find
^=^sin^— esin (^+45) + c, (8)
. ^_/^-/^i-e{sin(^ + 4o)-sin(^i + 45)}
sin ^— sin ^,
which gives the length of the liquid column so as to embrace a
given range of pressure. For example, let h — h^ = 22'o inches,
which is equivalent to 3 inches of mercury ; ^=90°, the greatest
angle at which the tube can be placed; 6-^ = lb°, the least angle
at which the tube can be conveniently placed; e = 4; then we
find A- = 30 inches nearly.
When 6 = 45°, equation (8) becomes A = A sin 45 — e + c. This
quantity, substituted for h in equation (7), gives the formula for
calculating approximately the range of the scale er. For ex-
ampk. let|: = y^, ^ = 62^, /^ = 82, ;; = 29-.5, ^ = 30, e = 4,
€=•4:; then we find q^ = 2'6, or the space of "13 of an inch to
each degree of temperature. Supposing, therefore, the instru-
ment to be made at mean temperature (62°), and mean pressure
(29-5), the liquid may fill the tube (standing at an angle of 45°)
to within 3 or 4 inches of the top. The globe may be about 2^
inches diameter ; length of tube S Q about 34 inches ; the dia-
meter of the tube about '3 of an inch ; and when the tube is held
in a vertical position, the liquid should cover the bottom of the
globe a little beyond the orifice of the tube leading from the
globe.
The temperature t being constant, r and 6 variable, the locus
of the point P will be expressed by the polar equation
r—k ,»
= — e sin 4o .
1 + cot 6*
At the limiting angle ^=15°, we find OC = 10 inches, and from
the foregoing equation, we find the maximum value of 0G=24
inches. The dimensions of M N may therefore be taiien as fol-
lows : viz. 0 N abo^it 12 inches, and 0 M about 26 inches. If
the pin 0 be placed a little higher, then 0 N should be a little
greater, and 0 M a little less.
Hastings, November 20, 1859.
[ 9 ]
II. On the Electric Deportment of the Flame of Alcohol.
By W. G. Hankel*.
NOTWITHSTANDING the numerous researches which,
down to the present time, have been published on the
electrical deportment of Hames and incandescent bodies, our
knowledge of most of these phsenomena is still very imperfect,
and we are for the most part uncertain as to their real causes.
The importance, for the theory of electricity, of correctly under-
standing these phsenomena, which are often very remarkable,
has induced me for some years past to submit them to a spe-
cial examination. Today I have the honour to lay before the
Physico-Mathematical Class of the Royal Society of Sciences a
fifth memoir t of my electrical researches, containing the results
I have obtained with respect to the flame of alcohol. I purpose
reserving for a later communication the discussion of the phse-
nomena which take place with other flames and with merely
glimmering bodies.
The present memoir divides itself into two principal parts.
The first comprises the researches on the electric tensions and
currents observed in the flame of alcohol ; the second treats of
the conduction of flames, and more particularly of the so-called
unipolar conduction discovered by P. Erman. I believe I am
justified in saying that in both respects I have succeeded in
tracing back the phsenomena to their true cause; and by means
of the simplicity thereby given to the results I have obtained,
it will be possible to give a brief and intelligible representation
of them.
In order to observe and measure the electrical tensions, I
made use of my electrometer J ; and for the currents, I used a
very sensitive galvanometer with 99G0 coils, and an astatic system
of two magnetic bars provided with a reflecting apparatus^.
When the flame of an alcohol lamp is put in communication
with the earth by means of a wire dipped into the lamp, and a
metal is placed in, over, or near the flame, the latter generally
becomes electric. "When, on the other hand, the metal situated
in or above the flame is connected with the earth, and the lump
insulated, the opposite electricity of the same tension is observed
on the wire immersed in the lamp.
* Trauslatoil from Pogjjeudoiff's Annalcn, vol. c-viii. p. 1-16, being a
paper commiuiicated by the Author to the Royal Scientific Society of
Saxony.
t Memoirs of the Royal Scientific Society of Saxony, vol. vii.
+ Marked A at p. 396 of vol. v. of the Memoirs of the Royal Scientific
Society of Saxony.
§ Described at p. 2fil of vol. vi. of the same Memoirs.
10 M. W. G. Hankel on the Electric Deportment
The nature and intensity of the electrical tension varies with
the nature of the metal placed in the lamp, as well as with that
of the metal above it.
But the nature and intensity of the electrical tension varies
also with the position of the metal above or in the flame.
When a thin plate of metal, standing at a considerable height
above the lamp, is made to approach the latter, so that it gra-
dually becomes more deeply immersed in the flame and more
intensely heated, the electricity first observed varies with this
change of position and becomes more negative; or if at first
positive, approaches the negative condition more and more. This
change may amount to more than the electromotive force of an
element formed of zinc, platinum, and alcohol.
No change of electric tension, however, takes place with the
change of position when the metal, on approaching or becoming
immersed in the flame, is prevented from taking a high tempe-
rature by ice being placed upon it; or when, instead of a
metal, a jet of water is passed through the flame.
Now in my memoir I give positive proof, by means of mea-
surements, that the electric tensions depend upon the act of
combustion only in so far as the gases and vapours of which the
flame consists form a conductor, which, like an ordinary liquid
conductor, is interposed between the metal situated in or above
the flame and the alcohol of the lamp. The mere act of com-
bustion does not produce electricity.
The electricity observed on the metals situated in or above
the flame, is nothing more than the tension at the end or pole
of a galvanic element having the selected metals for the solid,
and the alcohol together with the heated gases of the flame for
the liquid conductor.
The variations in the tensions as the metal gradually ap-
proaches the flame, are due solely to the increased temperature
of the metal, and to the consequent change of its position in
the so-called tension-series.
All metals by heating are moved towards the positive end of
the tension- series ; and when the metals are intensely heated, this
change in place may amount to more than the distance between
cold zinc and cold platinum, alcohol being employed as a liquid
conductor. For equal degrees of temperature, the amount of
this change is in all probability not very difi"erent in diflerent
metals.
If the ends or poles of the galvanic element, formed with
alcohol and flame as liquid conductors, upon which we formerly
observed free tensions, are joined together, an electric current is
produced in consequence of the electromotive power within the
circuit, whose direction is determined by the above tensions, and
of the Flame of Alcohol. 11
whose intensity depends also upon the resistance of the whole
circuit.
In the second part of my memoir I determine by exact mea-
surements the actions involved in the so-called unipolar conduc-
tion. The surfaces of contact of both poles of an element with
the flame in connexion with the earth being equal, a small por-
tion of positive electricity remains on the positive pole, whilst
the negative pole possesses the whole tension of the element
diminished by this small part.
Neither the electricity produced in the pole-surfaces by con-
ducting the flame to the earth, nor the tension conveyed to the
flame from one or more galvanic elements intentionally inter-
polated between it and the earth, change the previous results.
The electrical tensions Mhich appear at both poles are equal to
the sum of these electricities conveyed to the flame, and of the
tensions which would otherwise have existed there.
If the sui'face of one of the poles is increased, the tension of
this pole diminishes, whilst the tension of the opposite pole is
increased by the same amount. Exactly the reverse of this takes
place when the surface of one of the poles is gradually with-
drawn from the lamp.
The case in which an electrical opposition already exists be-
tween the metallic plates which serve as poles, required a special
explanation. This led to an examination of the tensions at the
poles of an unclosed galvanic element, when one metal stands in
a liquid opposite to two others which are of diff"erent electricities
and joined by a conductor. The tension of such an element
does not depend merely upon the position of the selected metals
in the tension-series, but also upon the resistance of the liquid
between the metals, or, to speak more correctly, upon the elec-
trical tension at the point of the tension-curve belonging to the
current between the connected metals, where the third metal is
immersed.
An elevation of the temperature of the pole-surfaces exer-
cises just as little influence upon the above-mentioned phaeno-
mena as does their chemical nature. Jets of water may be sub-
stituted for the metallic plates without producing any essential
diff"erence. AVith certain modifications, therefore, the pha?no-
mena of unipolar conduction also occur when the poles of a gal-
vanic element are connected, one by means of a metal, and the
other by being led to the alcohol of the lamp, with the flame
before it is put in communication with the earth.
If, after introducing two equal pole-surfaces of a galvanic
element into an insulated flame, the positive one is placed in
communication with the earth, the flame receives a negative ten-
sion equal to the above-mentioned residue. When the negative
12 On the Electric Deportment of the Flame of Alcohol.
pole is led to the earth, the flame receives a positive electricity
equal in amount to the whole tension of the element dimi-
nished by the small residue in question.
From what has already been said, it is easy to see in what
manner the tensions imparted to the flame vary with the size of
the conducting surfaces.
All the phsenomena of unipolar conduction may be simply
and completely explained by considering the tension-curve of the
closed circuit in question. In constructing this tension-curve,
it will be remarked that the curve on the metallic conductors,
on account of their comparatively small resistance, may be con-
sidered as running parallel to the abscissa-axis. The same holds
good approximately for the principal part of the flame. On the
other hand, owing to the diminution of the cross section, a
considerable resistance exists at the pole-surfaces in contact with
the flame, and consequently the ordinates of the above curve are
there perceptibly altered. Another remarkable result, however,
is that a pecuhar and very considerable hinderance is opposed to
the passage of negative electricity from solid or hquid conductors
into the flame, or to the entry of positive from the latter into
the conductors, which hinderance is diminished by enlarging the
surface of the negative pole. Whilst, then, the tension-cui've is
nearly parallel to the abscissa-axis along the metallic conductors
and the principal part of the flame, it sinks somewhat at the
positive pole, and at the negative through the whole remaining
portion of the tension of the element.
If, now, the flame is put in connexion with the earth, the metal
of the positive pole must receive a positive tension equal to the
previous small depression, and the metal of the negative pole a
negative tension equal to the depression at this pole.
If the positive pole is joined with the earth, a negative ten-
sion is produced in the flame equal to the small depression at
the positive pole. Lastly, if the negative pole is joined with the
earth, the flame shows a positive tension equal to the greater
depression at the negative pole.
The greater resistance which my experiments establish when
negative electricity passes into the hot rarefied gases of the flame,
also occurs, according to Ed. Becquerel, when an electric current
passes through very intensely heated air. I further show how
the fact leads to an explanation of the peculiar phsenomena ob-
served by Gaugain, when the two opposite currents of an induc-
tion apparatus pass through rarefied air.
The greater resistance at the negative pole explains too, lastly,
why a current ascends and descends the flame with different
degrees of facility.
When Andrews placed a spiral of platinum over the flame of
Mr. R. P. Greg on several New British Minerals. 13
a gas-lainp and joined it to one of the poles of a voltaic batteiy^
and the metallic tube of the lamp to the other, the current
passed more easily from the spiral through the flame to the lamp
than in the opposite direction. When a thin plate of platinum
is placed above the flame of an alcohol lamp, and one pole of
one or more elements is joined to it, and the other to a wire
immersed in the alcohol of the lamp, the eS"ects are more pre-
cisely the following : — If the thin plate of platinum is situated
high above the flame, the current passes more easily downwards
through the flame than upwards ; if the thin plate of platinum
is made to approach the flame, a position will be found in which
the current passes equally well in both directions ; at a still
greater proximity, the flame passes, on the contrary, more easily
upwards than downwards. The ratio of the intensities of the
currents conducted in opposite directions varies according to the
strength of the current.
The explanation of the efi'ects just described must be sought
in the peculiar resistance, before mentioned, at the negative pole.
At higher positions of the plate above the lamp, the conduction
of the flame is more perfect on the side of the wire ; at lower
positions this conduction is more perfect on the side of the
plate; and the current which passes through the flame between
the plate and the lamp must always possess greater intensity
when the negative pole acquires a relatively better conduction,
since its resistance is thereby diminished.
III. On several New British Minerals. By R. P. Greg, Esq.*
SINCE the publication of a ' Manual of the Mineralogy of
Great Britain and Ireland,^ by ^Ir. W. G. Lettsom and
myself, two years since, several species new to these countries
have been noticed, and which were not described in that work ;
they are anorthite, chrysoberyl, lepidomelane, Beraunite, and
Demidofiite ; the three former were noticed by Prof. Haughton
of Dublin, the two latter by myself.
1. Anorthite : occurs with hornblende and syenite at Carling-
ford Mountain, Co. Down. Analysis by Prof. Haughton : —
Silica 45-87
Alumina . . . . 34-73
Lime 17-10
Magnesia . . . I'oS
99-25
2. Chrysoberyl: said to occur in the granite of the Mourne
* Communicated bv the Atithor.
14 Mr. J. N. Hearder on Electrical Conductivity.
Mountains, (See the Quarterly Journal of the London Geolo-
gical Society for August 1856.)
3. Lepidomelane : a variety of uniaxial mica occurring in small,
flat, six-sided crystals, of a black colour, in the granite of Three
Rock Mountain, Co. Dublin.
This variety of mica contains an unusually large quantity of
the peroxides and protoxides of iron.
4. Beraunite, Breit : a variety of Delvauxene, supposed to be
a hydrous phosphate of peroxide of iron, resulting from the de-
composition of Vivianite. It has recently occun-ed at Wheal
Jane near Truro, in scaly and brittle masses, of a dark brownish-
red colour, intimately associated with crystallized and decom-
posing Vivianite, on eisen-nickelkies. My specimens came from
Mr. R. Tailing of Lostwithiel.
5. Demidoffite : a mineral recently described by Nordenskiold
as occurring with green malachite, chrysocolla, and phosphate of
copper, at Tagilsk in the Ural Mountains. It occurs at that
locality of a pale bluish-green colour, slightly earthy, and coat-
ing or encrusting the concentric layers of the mammillated ma-
lachite itself: H. 1-5 to 2-0. In the glass tube, yields water
with no acid reaction. Composition : —
Silica 31-55
Alumina .... 0*53
Oxide of copper . . 33*14
Magnesia . . . • 3*15
Water 2303
Phosphoric acid . . 10"22
101-62
Hitherto it seems that this mineral has been only noticed at
the Russian locality ; but I have in my collection characteristic
specimens, evidently of the same species, from Cumberland, and
also from a Cornish locality ; as well as from Valparaiso in South
America, with malachite and muriate of copper. At both our
British locahties it occurs with quartzose rock and malachite —
the latter, however, not in a mammillated state.
IV. Extracts from Notes on Electrical Conductivity.
By J. N. Heardek, Electrician, Plymouth*.
IT is generally acknowledged amongst electricians that the
term conduction, as applied to metals, implies negative
rather than positive qualities ; that is to say, all conductors
afford a certain amount of resistance, but those are considered
* Communicated bv the Author.
Mr. J. N. Hearder on Electrical Conductivity. 15
the best which afford the least. Upon this hypothesis, increased
transverse sectional area in the same metal diminishes resistance
by allowing the transmission of a larger quantity in a given time.
The practical determination of the relative conducting capabili-
ties of different metals, or of different samples of the same metal,
has generally been accomplished by the comparison of galvano-
metric or electro-magnetic effects ; but I am not aware of any
course of experiments which have been undertaken with a view
to trace any connexion, or institute any comparison, between the
thermal effects of the voltaic current on metals and their con-
ducting powers as thus indicated, or to work out any scale of
the conducting powers of metals, based simply upon the thermal
effects of the voltaic current upon them.
In 1826 Sir W. S. Harris communicated to the Royal Society
the result of a series of experiments with his thermo-electrometer
for determining the relative conducting power of metals for the
Leydeu discharge. His experiments were based upon the
assumption that metals are heated by equal discharges of elec-
tricity through them, from an electrical jar or battery, in pro-
portion to the resistance which they offer to its passage ; hence
their relative conducting powers in the scale were considered to
be inversely as their thermometric indications. Thus in passing
a carefully measured shock through wires of various metals, all
of precisely the same diameter and length, stretched through
the bulb of an air-thermometer, the relative degrees of heat in-
dicated upon the scale are shown in the following Table, exti'acted
from the Philosophical Transactions of 1827: —
Metals. Effects.
Copper 6
Silver 6
Gold 9
Zinc 18
Platinum 30
Iron 30
Tin 36
Lead 72
Brass 18
In the year 1827 I thought of using this thermo-electrometer
for determining the relative conducting powers of metals for
voltaic electricity, and was pleased, on applying a single pair of
plates to it for the first time, to find its indications extremely
regular, the fluid rising constantly to the same point at each
successive contact, and remaining almost permanent as long as
contact was maintained. The instrument, however, appeared to
require some few modifications to adapt it more particularly to
16 Mr. J. N. Hearder on Electrical Conductivity.
voltaic purposes; and after various trials I adopted the form
which I have described in the Philosophical Magazine for May
1857. The metals were all drawn into wires of the same size,
and the same lengths were used in each experiment.
The voltaic batteries which I used were formed upon the prin-
ciple of Dr. Harems calorimotor and coil batteries. One modifi-
cation consisted of a plate of zinc 6 inches wide and 6 feet in
length, coiled with a similar plate of copper between its convolu-
tions so as to maintain a sphere of half an inch between the cop-
per and zinc, the last coil of copper being made entirely to
enclose the end of the zinc, so that the copper plate was about
six inches longer than the zinc. Both surfaces of each metal
were thus opposed to the action of the others. A second form
consisted of a similar area of zinc and copper cut into plates of
6 inches square^ and fastened alternately in grooves in a wooden
frame at a distance of half an inch from each other, the two end
plates being copper. All the zinc plates were united on one side,
and all the copper plates on the other, thus forming a single
pair equal in surface and, as ascertained by experiment, equal in
efi'ect to the coil just described. These batteries were suspended
over a wooden trough by counterbalancing weights, which ad-
mitted of their being immersed either wholly or to any depth in
the acid.
The exciting fluid consisted, by measure, of sulphuric acid 1
part, nitric acid 1 part, and water 120. Stout flexible wires
proceeded from the battery to the thermo-electrometer, and the
battery was plunged in the acid at each experiment and raised
again as soon as it was concluded. The results which I shall
have to detail are rather incomplete in their character, as they
are merely the remains of some scattered memoranda, a great
number of which were mislaid owing to the accident which some
two or three years after deprived me of sight. I am induced,
however, to publish such as I have, since I cannot discover in
my intercourse with electricians that the facts are even now
generally known. I briefly alluded to these experiments on a
former occasion (see paper " On Induction Coil" in the Philo-
sophical Magazine, May 18.o7, p. 332, note).
I shall forbear to enter into the rationale of the phenomena,
but allow the simple facts to be taken for as much as they are
worth.
In my first series of experiments I was met by the curious fact,
that the order in which the metals were heated by the voltaic
arrangements which I employed, was the reverse of that which
took place with the Leydeu discharge ; that is to say, the best
conductors were the most heated, and the worst the least, as will
be seen by the following Table, in which the length of wire
Mr. J. N. Hearder on Electrical Conductivity. 17
employed in each experiment was 3*5 inches, and its size about
No. 26 wire-gauge. The numbers given are the mean of six
experiments, the variation in them not exceeding more than 2
or 3 degrees : —
Metal employed in Degrees of heat on scale
thermo-electrometer. of thermo-electrometer.
Silver 81
Copper 70
Zinc 47
Brass 43
Gold 41
Platinum 41
Tin 39
Iron 35
Lead 26
These experiments were repeated at different times with the
same wires and with the same relative results.
Since the best conductors were the most heated in these ex-
periments, it seemed to follow that, with any single metal, larger
wires would be heated more than small ones ; and this I found
to be the case up to the largest size that could be inserted into
the electrometer, viz. No. 15 wire-gauge. I regret that a scale
of these results with copper wires from No. 15 to No. 36 has
been lost, but it showed a curious coincidence between the tem-
perature and the mass of metal. This remarkable inversion of
their relative order as compared with the results obtained by the
Leyden discharge, whilst it showed a consistency with itself
which left no room to attribute it to any error in manipulation,
yet seemed to exhibit such an inconsistency with preconceived
notions of the laws of electrical conduction, that I was induced
to vary the experiments in the following manner.
Instead of introducing the several metallic wires in succession
into the bulb of the thermo-electrometer, I used them externally,
causing them to form part of the circuit between it and the bat-
tery, and employing in the electrometer simply a copper wire
niTich stouter than those under examination. The following
Table gives the results, the same wires being used as before : —
Wires in circuit between Degrees on
battery and thermometer. thermometer.
Silver 142
Copper 128
Zinc 93
Brass 92
Gold 70
Tin 61
Platinum 60
Iron 55
Lead 33
Phil. Mag. S. 4. Vol. 19. No. 124. Jan. 1860. C
18 Mr. J. N. Hcavder on Electrical Conductivity .
Note. — The battery being applied to the electrometer without
any of the wires in circuit, the fluid in the stem rose to 176°.
These experiments were repeated at various intervals with
wires made indiscriminately from such samples as were at hand,
though not with any idea of testing variations in the conducting
power of different samples of the same metal ; hence the relation
between the order of the results was not always the same, as will
be seen by the following set of experiments, in which a different
set of wires were employed : —
Table I.
Wires in the bulb of Degrees indicated
the thermometer. on the scale.
Copper 180
Zinc 156
Brass 155
Platinum ...... 128
Tin 126
Iron 110
Lead 104
Table II.
Wires introduced Degrees on thermo-electrometer
into the circuit. containing copper wire.
Circuit completed without wire . 150
Copper 128
Zmc 93
Brass 92
Tin 61
Platinum 60
Iron 55
Lead 33
The discrepancy in these results, though perplexing at the
time, is now easily accounted for, when it is considered that even
samples of copper wire vary as much in their conducting power
as 50 to 120.
On employing two electrometers in consecutive circuit, in
one of which was inserted a stout copper wire, and in the other
the various metals in succession, it was curious to observe the
fluid stand highest in both when the best conductors were used,
and lowest with the worst ; whilst on employing a similar
arrangement for transmitting the charge of an electrical battery
the order was reversed, each electrometer giving the highest
when the other gave the lowest results.
Whilst experimenting on one occasion with the various wires
externally to the electrometer, I had the curiosity to bring my
finger in contact with the wire to ascertain its temperature. I
On the Mutiom and Collisions of Perfectly Elastic Spheres. 1 9
remarked that every time I touched it the fluid in the electro-
meter rose, indicating an increase of temperature, and implying
also an increase of conducting power in the metal thus touched.
I found that this was owing to a reduction of its temperature ;
for on subsequently moistening it with ether, water, &c., or by
blowing upon it, the fluid rose in the electrometer as the tem-
perature was reduced, whilst the application of a spirit-lamp to
increase the tem})erature of the wire produced a corresponding
fall in the thermometer. Two electrometers were subsequently
employed in circuit, the same current passing consecutively
through them. To one of the electrometers a second battery
was applied. The result was an increase of temperature of the
included wire ; and I discovered that, by raising or lowering the
second battery so as to gradually increase or diminish the tem-
perature of one of the wires, the fluid as it rose and fell in that
electrometer gave rise to a reverse motion of the fluid in the
other, so that as one rose the other fell, and vice versa.
Although these experiments were made more than thirty
years since, I am induced to believe that they may still appear
novel to some, since, in a conversation a short time since with
one of the first electricians of the day, he would scarcely credit
them, alleging that they were contrary to all our experience ;
they must, however, be taken as indicating only the results due
to the peculiar arrangements and conditions herein described.
V. Illustrations of the Dynamical Theory of Gases. — Part I.
On the Motions and Collisions of Perfectly Elastic Spheres.
By J. C. Maxwell, M.A., Professor of Natural Philosophy
in Marischal College and University of Aberdeen*.
^0 many of the properties of matter, especially when in tlie
^ gaseous form, can be deduced from the hypothesis that
their minute parts are in rapid motion, the velocity increasing
with the temperature, that the precise nature of this motion
becomes a subject of rational curiosity. Daniel Bernouilli, Hera-
path, Joule, Kronig, Clausius, &c. have shown that the relations
between pressure, temperature, and density in a perfect gas can
be explained by supposing the particles to move with uniform
velocity in straight lines, striking against the sides of the con-
taining vessel and thus producing pressure. It is not necessary
to suppose each particle to travel to any great distance in the
same straight line ; for the cft'ect in producing pressure will be
the same if the particles strike against each other; so that the
straight line described may be very short. M. Clausius has de-
termined the mean length of path in terms of the average distance
* Communicated by the A\itlior, bavins betMi read at tbe Meeting of the
Britisb Association at Al)crclepn, September 21, 185!'.
C 2
20 Prof. Maxwell un the Motiuns and Collisions
of the particles, and the distance between the centres of two par-
ticles when collision takes place. We have at present no means
of ascertaining either of these distances; but certain phsenomena,
such as the internal friction of gases, the conduction of heat
through a gas, and the diffusion of one gas through another,
seem to indicate the possibility of determining accurately the
mean length of path which a particle describes between two suc-
cessiv^e collisions. In order to lay the foundation of such inves-
tigations on strict mechanical principles, I shall demonstrate the
laws of motion of an indefinite number of small, hard, and per-
fectly elastic spheres acting on one another only during impact.
If the properties of such a system of bodies are found to cor-
respond to those of gases, an important physical analogy will be
established, which may lead to more accurate knowledge of the
properties of matter. If experiments on gases are inconsistent
wdth the hypothesis of these propositions, then our theory,
though consistent with itself, is proved to be incapable of ex-
plaining the phenomena of gases. In either case it is necessary
to follow out the consequences of the hypothesis.
Instead of saying that the particles are hard, spherical, and
elastic, we may if we please say that the particles are centres of
force, of which the action is insensible except at a certain small
distance, when it suddenly appears as a repulsive force of very
great intensity. It is evident that either assumption will lead
to the same results. For the sake of avoiding the repetition of
a long phrase about these repulsive forces, I shall proceed upon
the assumption of perfectly elastic spherical bodies. If we sup-
pose those aggregate molecules which move together to have a
bounding surface which is not spherical, then the rotatory mo-
tion of the system will store up a certain proportion of the whole
vis viva, as has been shown by Clausius, and in this way we may
account for the value of the specific heat being greater than on
the more simple hypothesis.
On the Motion and Collision of Perfectly Elastic Spheres.
Prop. I. Two spheres moving in opposite directions with velo-
cities inversely as their masses strike one another ; to determine
their motions after impact.
Let P and Q be the position
of the centres at impact ; A P,
B Q the directions and magni-
tudes of the velocities before
impact ; V a, Qb the same after
impact; then, resolving the ve-
locities parallel and perpendi-
cular to P Q the line of cen-
tres, we find that the velocities parallel to the line of centres are
of Perfectly Elastic Spheres, 21
exactly reversed, while those perpendicular to that line are un-
changed. Compounding these velocities again, we find that the
velocity of each ball is the same before and after impact, and
that the directions before and after impact lie in the same plane
with the line of centres, and make equal angles with it.
Prop. IT. To find the probability of the direction of the velo-
city after impact lying between given limits.
In order that a collision may take place, the line of motion of
one of the balls must pass the centre of the other at a distance
less than the sum of their radii ; that is, it must pass through
a circle whose centre is that of the other ball, and radius {s) the
sum of the radii of the balls. Within this circle every position
is equally probable, and therefore the probability of the distance
from the centre being between r and r -|- dr is
2rdr
Now let ^ be the angle APa between the original direction and
the direction after impact, then APN = -2-0, and 7'=ssin~(f>, and
the probability becomes
I sin (f) d<f>.
The area of a spherical zone between the angles of polar distance
<f) and (f) + d(f) is
27r sin (f> dxf) ;
therefore if o) be any small area on the surface of a sphere, radius
unity, the probability of the direction of rebound passing
through this area is
so that the probability is independent of ^, that is, all directions
of rebound are equally likely.
Prop. III. Given the direction and magnitude of the veloci-
ties of two spheres before impact, and the line of centres at im-
pact; to find the velocities after impact.
Let O A, 0 B re-
present the veloci-
ties before impact,
so that if there had
been no action be-
tween the bodies
they would have
been at A and Battheendof a second. Join A B, and let G be their
centre of gravity, the position of which is not affected by their
mutual action. Draw G N parallel to the line of centres at im-
l)act (not necessarily in the plane A OB). Draw nGh \u the
22 Prof. Maxwell on the Motions and Collisions
plane AGN, making N G c = N G A, and G « = G A and GZ» = GB;
then by Prop. \. G a and G b will be the velocities relative to G ;
and compounding these with 0 G, we have 0 a and O b for the
true velocities after impact.
By Prop. II. all directions of the line aGb are equally pro-
bable. It appears therefore that the velocity after impact is
compounded of the velocity of the centre of gravity, and of a
velocity equal to the velocity of the sphere relative to the centre of
gravity, which may with equal probability be in any direction
whatever.
If a great many equal spherical particles were in motion in
a perfectly elastic vessel, collisions would take place among the
particles, and their velocities would be altered at every collision ;
so that after a certain time the vis viva will be divided among the
particles according to some regular law, the average number of
particles whose velocity lies between certain limits being ascer-
tainable, though the velocity of each particle changes at evei-y
collision.
Prop. IV. To find the average number of particles whose velo-
cities lie between given limits, after a great number of collisions
among a great number of equal particles.
■ Let N be the whole number of particles. Let x, y, z be the
components of the velocity of each particle in three rectangular
directions, and let the number of particles for which x lies be-
tween X and x-^dx\i& '^f{x)dx, wliei*e/(a?) is a function of x to
be determined.
The number of particles for which y lies between y and y + dy
will be N/(y)c(y ; and the number for which z lies between z and
z + dz will be 'Nf{z)dz, where / alw^ays stands for the same
function.
Now the existence of the velocity x does not in any way aflfect
that of the velocities y or z, since theSe are all at right angles to
each other and independent, so that the number of particles
whose velocity lies between x and x + dx, and also between j/and
y + dy, and also between z and z + dz, is
m^)fiy)f{z)dvdydz.
If we suppose the N particles to start from the origin at the
same instant, then this will be the number in the element of
volume {dxdy dz) after unit of time, and the number referred to
unit of volume will be
W{^)Ay)A^)-
But the directions of the coordinates are perfectly arbitrary, and
therefore this number must depend on the distance from the
origin alone, that is
of Perfectly Elastic Spheres. 23
Solving this fuuctioual equation, we find
/(.r) = Ce-^^ <^(;-2)=CV^'.
If we make A positive, the number of particles will increase
with the velocity, and we should find the whole number of par-
ticles inlinite. We therefore make A negative and equal to
5, so that the number between x and x-\-da:'\%
a.
NCe ofldx.
Integrating from <r= -co to x=- -\- cc , we tind the whole num-
ber of particles.
f{x) is therefore
7^ c
a V TT
Whence we may draw the following conclusions : —
1st. The number of particles whose velocity, resolved in a cer-
tain direction, lies between x and x-\-dx is
^^~e-idx (1)
« v'tt «•
2nd. The number whose actual velocity lies between v and
v + dv is
N— ^w«e~S</f (2)
3rd. To find the mean value of v, add the velocities of all the
particles together and divide by the number of particles; the
result is
mean velocity = — =. (3)
4th. To find the mean value of r^, add all the values together
and divide by N,
mean value of iJ^=|a'^ (-i)
This is greater than the square of the mean velocity, as it
ought to be.
It appears from this proposition that the velocities are distri-
buted among the particles according to the same law as the
errors are distributed among the observations in the theory of
the " method of least squares," The velocities range from 0 to
X , but the number of those having great velocities is compara-
tively small. In addition to these velocities, which are in all
directions equally, there may be a geiu^ral niotion of translation
24 Prof. Maxwell on the Motions and Collisions
of the entire system of particles which must be compounded with
the motion of the particles relatively to one another. We may
call the one the motion of translation, and the other the motion
of agitation.
Prop. V. Two systems of particles move each acco ding to the
law stated in Prop. IV. ; to find the number of pairs of particles,
one of each system, whose relative velocity lies between given
limits.
Let there be N particles of the first system, and N' of the
second, then NN' is the whole number of such pairs. Let us
consider the velocities in the direction of x only ; then by
Prop. IV. the number of the first kind, whose velocities are be-
tween X and x-\-dx, is
N = e~^dx,
a V'tt
The number of the second kind, whose velocity is between x-\-y
and A' + y + dy, is
1 _'£±l^
N'^— -^e ^^ dy,
where /3 is the value of a for the second system.
The number of pairs which fulfil both conditions is
NN'-g-e W P^ Jdxdy.
apir
Now X may have any value from — x to +x consistently with
the difference of velocities being between y and y + dy ; therefore
integrating between these limits, we find
NN' /-TT-^V^"^'^y .... (5)
Va'^ + p VTT
for the whole number of pairs whose difference of velocity lies
between y and y + dy.
This expression, which is of the same form with (1) if we put
NTs' for N, ci^ + ^'^ for a^, and y for x, shows that the distribu-
tion of relative velocities is regulated by the same law as that of
the velocities themselves, and that the mean relative velocity is
the square root of the sum of the squares of the mean velocities
of the two systems.
Since the direction of motion of every particle in one of the
systems may be reversed without changing the distribution of
velocities, it follows that the velocities compounded of the velo-
cities of two particles, one in each system, are distributed accord-
ing to the same formula (5) as the relative velocities.
Prop. VI. Two systems of particles move in tlic same vessel ;
of Perfectly Elastic. Spheres.
25
to prove that the mean vis viva of each particle will become the
same in the two systems.
Let P be the mass of each particle of the first system, Q that
of each particle of the second. Let p, q be the mean velocities
in the two systems before impact, and let
p',q'he the mean velocities after one impact.
Let AO=p and OB = q, and let A O B be
a right angle ; then, by Prop. V., A B will be
the mean relative velocity, 0 G will be the
mean velocity of centre of gravity ; and
drawing a G 6 at right angles to 0 G, and
making a G = AG and 6G = BG, then Oa
will be the mean velocity of P after impact,
compounded of 0 G and G a, and 0 b will
be that of Q after impact.
Now
AB= s/^Tf, AG= ^ ^/^+f, ^^= PTQ '^^^'
OG = /^^V + QV
therefore
P + Q
p' = Oa:
and
and
P + Q
^ P + Q
Py^-Qr/^=(^-^)'(P;,^_Qg^)
(6)
It appears therefore that the quantity Vp'^ — Qq^- is diminished
at every impact in the same ratio, so that after many impacts it
will vanish, and then
Pp2^Qg2.
Now the mean vis viva is -Pa^= -rj-Pjy^ for P, and -^ Qo'^ for
* o o
Q ; and it is manifest that these quantities will be equal when
\y = Qq^.
If any number of diflferent kinds of particles, having masses
P,Q,R, and velocities j9, ^r, ?• respectively, move in the same
vessel, then after many impacts
P/v^ = Qry^ = Rr5, &c (7)
Prop. VII. A particle moves with velocity ;• relatively to a
number of particles of which there arc N in unit of volume ; to
26 Prof. Maxwell on the Motions and Collisions
tind the number of these which it approaches within a distance
i' in unit of time.
If we describe a tubular surface of which the axis is the path
of the particle, and the radius the distance s, the content of this
surface generated in unit of time will be irrs^, and the number
of particles included in it will be
Nth-^^ (8)
which is the number of particles to which the moving particle
approaches within a distance s.
Prop. VIII. A particle moves with velocity zj in a system
moving according to the law of Prop. IV. ; to find the number of
particles which have a velocity relative to the moving particle
between r and r + dr.
Let u be the actual velocity of a particle of the system, v that
of the original particle, and /• their relative velocity, and 6 the
angle between v and r, then
m2 = ^2_|_^.2_9i-,-C0S 6.
If we suppose, as in Prop. IV., all the particles to start from the
origin at once, then after unit of time the " density " or number
of particles to unit of volume at distance u will be
From this we have to deduce the number of particles in a shell
whose centre is at distance r, radms = r, and thickness =(/r,
^—^-\e-^!^-e-^\dr, ... (9)
which is the number requned.
Cor. It is evident that if we integrate this expression from
?- = 0 to r=x , we ought to get the whole number of particles
= X, whence the following mathematical result,
\ da:.x{e «- —e~ «' )= ^iract. . . (10)
Prop. IX. Two sets of particles move as in Prop. V. ; to find
the number of pairs which approach within a distance s in unit
of time.
The number of the second kind which have a velocity between
r and v-'t-dv is
X'— ^rVi^i.— n'.
The number of the first kmd whose vclocitv relative to these is
of Perfectly Elastic Spheres. 27
between r and r + dr is
1 r -^"^^ _(r+t>y^
N =-(e a2 — g a2 )f/,.= H,
a >v/7r ^^
and the number of pairs which approach within distance s in
unit of time is
n Ti'irrs'^,
'—^sh'He ^le n- — e «=* U
By the last proposition we are able to integrate with respect
to V, and get
NN' '^^^ 5Ve-«2+/32 ^^.
Integrating this again from r = 0 to ;■ = « ,
2NN'A/7rv/a2 + yS-2s' (11)
is the number of collisions in unit of time which take place in
unit of volume between particles of different kinds^ s being the
distance of centres at collision. The number of collisions be-
tween two particles of the first kind^ s^ being the striking
distance, is
and for the second system it is
The mean velocities in the two systems are — -^ and -^^^ ; so
that if li and l^ be the mean distances travelled by particles of
the first and second systems between each collision, then
J =7rN, v2s,-' + 7riSc, s%
'i a
Prop. X. To find the probability of a ])article reaching a
given distance before striking any other.
Let us suppose that the probability of a particle being stopped
while passing through a distance rfa', is acLv ; that is, if N par-
ticles arrived at a distance x, ^ud,r of them would be stopped
before getting to a distance .r + da. Putting this mathematically,
dy ^, ^. ,,
-p-=— >a, or i\=Lc~'^.
dx
28 Prof. Maxwell on the Motions and Collisions
Putting N = l when a? = 0, we find e~" for the probability of a
particle not striking another before it reaches a distance x.
The mean distance travelled by each particle before striking is
-=/. The probability of a particle reaching a distance = nl
a
without being stmck is e"". (See a paper by M. Clausius, Phi-
losophical Magazine, February 1859.)
If all the particles are at rest but one, then the value of a is
where s is the distance between the centres at collision, and X
is the number of particles in unit of volume. If v be the velo-
city of the moWng pai-ticle relatively to the rest, then the num-
ber of colhsions in unit of time will be
and if i\ be the actual velocity, then the number will be rja ;
therefore
where i\ is the actual velocity of the striking particle, and v its
velocity relatively to those it strikes. If v^ be the actual velocity
of the other particles, then v= s/v^^-^v^^. If i-i = r.2, then
v= V2i\, and
«= 'v/27rs2X.
Xote. — M. Clausius makes a = |7rs^X.
Prop. XI. In a mixture of particles of two diflferent kinds, to
find the mean path of each particle.
Let there be Nj of the first, and Xg of the second in unit of
volume. Let s^ be the distance of centres for a colUsion between
two particles of the first set, s^ for the second set, and 5-' for col-
lision between one of each kind. Let v^ and Zg be the coefficients
of velocity, Mj M2 the mass of each particle.
The probabdity of a particle Mj not being struck till after
reachin"- a distance x-^ by another particle of the same kind is
g— ■^TTSl-'SlX
The probability of not being struck by a particle of the other
kind in the same distance is
Therefore the probability of not being struck by any particle
before reaching a distance a; is
of Perfectly Elastic Spheres. 29
and if /, be the mean distance for a particle of the first kind,
i-~. ./27r.i^2j^, + 7rV^l+^,6-'2N2. . . (12)
Similarly, if ^ be the mean distance for a particle of the second
kind,
\= >/27r./N, + 7rv/l+ J^^'^^N,. . . (13)
The mean density of the particles of the first kind is NiMi=/3„
and that of the second N2M2 = P2- ^^ ^^ P^*
"=^^1; (")
i = Ap, + Bpj, l=Cp, + Dp«, . . (13)
and
G-ll,v,-v,^ ^'^^
Prop. XII. To find the pressure on unit of area of the side of
the vessel due to the impact of the particles upon it.
Let N = number of particles in unit of volume ;
M = mass of each particle ;
V = velocity of each particle ;
/ 3= mean path of each particle ;
then the number of particles in unit of area of a stratum dz
'^'''^''' ^d. (17)
The number of collisions of these particles in unit of time is
N^^^ (18)
The number of particles, which after collision reach a distance be-
tween nl and {n + dn)l, is
ISi-e-'^dzdn (19)
The proportion of these which strike on unit of area at distance
t?- (-)
the mean velocity of these in the direction of z is
30 Prof. Maxwell on the Motions and CuUisions
Multiplying together (19), (20), and (21), and M, we find the
momentum at impact
Integrating with respect to z from 0 to 7il, we get
^M^v^ ne-" dn.
Integrating with respect to n from 0 to oo , we get
^MXf2
for the momentum in the direction of z of the stinking particles ;
the momentum of the particles after impact is the same, but in
the opposite direction; so that the whole pressure on unit of area
is twice this quantity, or
;? = ;^MNr2 (22)
This value of p is independent of / the length of path. In
applying this result to the theory of gases, we put MN=p, and
t'^ = 3/t, and then
p = kp,
which is Boyle and Mariotte's law. By (4) we have
^•2=|a^ .'.a^ = 2k (23)
We have seen that, on the hypothesis of elastic particles
moving in straight lines, the pressure of a gas can be explained
by the assumption that the square of the velocity is proportional
directly to the absolute temperature, and inversely to the specific
gravity of the gas at constant temperature, so that at the same
pressure and temperature the value of NMi^^ is the same for all
gases. But we found in Prop. VI. that when two sets of par-
ticles communicate agitation to one another, the value of Mf^ is
the same in each. From this it appears that N, the number of
particles in unit of volume, is the same for all gases at the same
pressure and temperature. This result agrees with the chemical
law, that equal volumes of gases are chemically equivalent.
We have next to determine the value of /, the mean length of
the path of a particle between consecutive collisions. The most
direct method of doing this depends upon the fact, that when
different strata of a gas slide upon one another with different ve-
locities, they act upon one another with a tangential force tend-
ing to prevent this sliding, and similar in its results to the fric-
tion between two solid surfaces sliding over each other in the
same way. The explanation of gaseous friction, according to
our hypothesis, is, that particles having the mean velocity of
translation belonging to one layer of the gas, pass out of it into
another layer having a diflferent velocity of translation ; and by
striking against the particles of the second layer, exert upon it
of Perfectly Elastic Spheres. 31
a tangential force which constitutes the internal friction of the
gas. The whole friction between two portions of gas separated
by a plane surface, depends upon the total action between all the
layers on the one side of that surface upon all the layers on the
other side.
Prop. XIII. To find the internal friction in a system of moving
particles.
Let the system be divided into layers parallel to the plane of
xy, and let the motion of translation of each layer be u in the
direction of .r, and let M = A + B2r. We have to consider the
mutual action between the layers on the positive and negative
sides of the plane xy. Let us first determine the action between
two layers dz and dz', at distances z and — z' on opposite sides
of this plane, each unit of area. The number of particles which,
starting from dz in unit of time, reach a distance between nl and
{n + dn)l is by (19),
'N -^e'^^dzdn.
The number of these which have the ends of their paths in the
layer dz' is
^ -^e-"dzdz'dn.
The mean velocity in the direction of x which each of these has
before impact is A + B^, and after impact A + Bz'; and its mass
is M, so that a mean momentum =MB{z—z') is communicated
by each particle. The whole action due to these collisions is
therefore
NMB / „ (z-z')e-^ dz d^ dn.
We must first integrate with respect to z' between 2'' = 0 and
z' = z — nl; this gives
^NMB ^ {nV^-z^)e-" dz dn
for the action between the layer dz and all the layei-s below the
plane xy. Then integrate from z=0 to zssnl,
^MNB/wi^e-" dti.
Integrate from n = 0 to 71 = 00, and we find the whole friction
between unit of area above and below the plane to be
F = ;MN/i;B=>p/i;$^=/x^,
^ '^ dz '^ dz'
where /i, is the ordinary coefficient of internal friction,
32 Prof. H. Rose on the different States of Silicic Acid,
where p is the density, / the mean length of path of a particle,
and V the mean velocity v=- — r= =2a / — ^
Now Professor Stokes finds by experiments on air,
\/^ = -116.
If we suppose \//; = 930 feet per second for air at 60°, and
therefore the mean velocity i;=1505 feet per second, then the
value of /, the mean distance travelled over by a particle between
consecutive collisions, = ^^yVo o^^ ^^ ^^ inch, and each particle
makes 8,077,200,000 collisions per second.
A remarkable result here presented to us in equation (24), is
that if this explanation of gaseous friction be true, the coefiicient
of friction is independent of the density. Such a consequence of
a mathematical theory is very startling, and the only experiment
I have met with on the subject does not seem to confirm it. We
must next compare our theory with what is known of the diffusion
of gases, and the conduction of heat through a gas.
[To be continued.]
VI. On the different States of Silicic Acid. By M. H. Rose *.
N'UMEROUS determinations of the density of silicic acid,
and especially those of Count Schaffgotsch, prove that
there exist two distinct modifications of this acid, one of which
has a density of 2'6, whilst in the other the density rises to 2'2,
or 2"3. The first is always crystallized, or more or less crystal-
line, the second always amorphous.
Crystallized silica is found not only in rock-crystal, quartz,
amethyst, sandstone, and quartzose sand, but also in a great
number of the varieties of silica, in appearance compact, but
really formed of an aggregation of crystalline particles, as their
property of polarizing light proves — such ai-e chalcedony, chryso-
prase, jasper, flint, and certain siliceous woods. Some of these
varieties may contain traces of water or foreign matter, which
make their density vary a little, without, however, causing the
same to fall below 2'6.
The chemical and physical properties of all these substances
are exactly the same. If crystallized quartz seems to resist some-
* The original memoir by Prof. H. Rose will be found in PoggendorfF's
Annalen, September 1859. The present abstract is translated from the
Bibliotheque Universelle for Sept. 20th, 1859.
and on the Origin of Granites. 33
what more the action of chemical agents, such as hydrofluoric acid
or caustic potash, it is easy to see that this sHght difference depends
only upon the great cohesion which a more perfect crystallization
determines. In fact, rock-crystal and silica, both reduced to an
extremely fine powder, do not present any difference. It is
almost beyond doubt that the varieties of compact and crystal-
line silica, such as flint, agate, and siliceous woods, have been
formed in the humid way. The preservation of the ligneous
structure in these last, the presence of infusoria in flint, signal-
ized by Ehrenberg, the transformation of a great number of
fossils into flint, are sufficient proofs. A great number of facts
also prove that rock-crystal and ordinary quartz, which have the
same density, can only have been formed in the hiimid way,
or at least by the influence of water.
We have succeeded by various modes of treatment, but only
in the humid way, in obtaining crystallized silicic acid in the
form of quartz. M. de Senarmont has obtained this result by
heating, in a closed vessel at 200" or 300°, a solution of silicic
acid in water acidulated by carbonic or hydrochloric acid.
M. Daubree has obtained silica in a crystalline state by the
action of the vapour of water on chloride or fluoride of silicium at
a red heat ; afterwards he obtained it in distinct crystals by the
action of water upon glass, under the influence of an elevated
temperature and high pressure.
The frequent association, in several formations, of crystallized
quartz with silica in a compact crystalline state, also shows that
it must have been formed in the humid way.
On the contrary, notwithstanding several attempts, we have
never succeeded in obtaining by means of heat crystallized or
compact crystalline silica.
But the strongest argument against the supposition that quartz
has passed through the state of igneous fusion before its crystal-
lization, is found in the fact that quartz passes by fusion into
the amorphous condition whose density is 2 "2.
The fusion of quartz has often been effected, by Davy, Clarke,
Stromeyer, and Marcet, more recently also by Gaudin and De-
ville. In every case, after this fusion, silica is completely amor-
phous and vitreous, its density being 2*2. If the objection is
raised, that fused quartz might have passed into a crystalline
state by an extremely slow cooling, one may reply that it is im-
possible that a granitic mass can have cooled with the same slow-
ness throughout its whole extent ; there must necessarily have
been portions exposed to a more rapid cooling ; so that here and
there the amorphous modification of quartz ought to be found.
But its presence has never been detected ii^ rocks. It has some-
times been supposed that the crystallization might have been
Phil. Mag. S. 4. Vol. 19. No. 124. Jan. 18G0. D
34 Prof. II. Hose on the different States of Silicic Acid,
produced by the action of a very elevated temperature below
the point of fusion, as occurs sometimes in the devitrification
and crystallization of g;lass. Some experiments of Prof. Rose
show the equal impossibility of sustaining this view. These ex-
periments were made in a porcelain kiln, where the temperature
rises to and remains during eighteen hours at about 2000° Centi-
grade (according to M. Eisner), after which the substances thus
heated cool very slowly.
A crystal of quartz perfectly transparent did not undergo any
alteration by this test; its density of 2'651 was afterwards found
to be 2"650. A crystal of the same quartz, the angularity of
which was intact, but the inferior extremity of which was cracked,
did not sustain any alteration in the intact portion, but became
whitish and brittle in the part which was already fissured. Those
portions which had become opaline, possessed a density of 2'613,
which indicated the passage of the quartz to a modification less
dense. Lastly, a ci'ystal of very pure quartz was submitted to
the same test, after having been previously reduced to a very fine
powder. This powder subsided consideiably, without however
cohering, and its density fell to 2-394 It was exposed a second
time in the furnace, and the density became 2'329.
A fragment of blackish iiint, density 2"591, was submitted to
the same process. Without changing its form, it became white
and capable of very easy pulverization. The density of an entire
fragment was found to be 2"218 ; that of the fine powder
2-237.
It results from these experiments that crystallized silica passes
gradually into the amorphous modification when it is exposed to
an elevated temperature below its point of fusion. They prove
also that a more perfect crystalline state opposes a greater
resistance to this transformation, as it does to the action of
solvents.
The amorphous modification is not produced merely by the
action of great heat upon crystallized silica ; it is obtained also on
fusing the same with an alkali and afterwards decomposing the
alkaline silicate by an acid, and generally whenever a natural or
artificial silicate is decomposed by an acid.
Here the author signalizes various phsenomena which are ob-
served during this decomposition. Sometimes the silica remains
in solution, sometimes it becomes separated in the pulverulent
state, sometimes it determines the coagulation of the liquor into
a gelatinous mass. He also signalizes the influence of calcina-
tion on certain silicates, — sometimes rendering undecomposable
by acids those which were previously decomposed with facility,
sometimes, on the contrary, facilitating their decomposition.
These facts have led certain chemists to suppose the existence of
and on the Or if/ in of Granites, 3.")
two distinct moditicatioiis of silicic acid in silicates. Whatever
the value of this hypothesis may be, it results from the experi-
ments of M. Rose, that, whatever may be the condition in which
silica presents itself at the time of the decomposition of the sili-
cates by acids, it possesses always the same properties. Its
density is about 2*2, and rises to 2'3 by a somewhat prolonged
calcination.
The silica produced by the action of water on the gaseous
fluoride of silicium, presents the same characters.
The shells of infusoria are also formed of amorphous silica of a
density of 2"2, rising to 2 "3 by calcination in a porcelain kiln.
The two modifications of silica are not merely distinguished
by their density ; they differ very much in the resistance which
they oppose to solvents. Solutions of caustic alkalies and alka-
line carbonates, as well as hydrofluoric acid, dissolve the amorphous
silica with very great facility when compared with crystalline
silica; this remark applies also to quartz rendered amorphous by
fusion, as well as to amorphous silica obtanied in the humid way.
Amorphous silica is found in nature in the form of opal and
hyalite. These minerals possess a density of about 2"14 to
2*16. But these rather low numbers depend upon the fissured
structure of the minerals ; for when their density is determined
after having reduced them to a very fine powder, it is found to
be about 2"2.
Although opal is frequently found in plutonic rocks, as in
basalts, it has probably not been formed there in a fused mass,
but rather been produced by the prolonged action of water on
the rocks. Besides, it is also found in rocks which certainly
have not had an igneous origin — in the interior of fossils for
instance. It is very often associated with the variety of silica
whose density is 2 '6. It has probably been formed by the soli-
dification of a deposit of gelatinous silica, whilst the crystalline
variety might have resulted from the slow deposit of silica in
actual solution.
That which is sometimes found in the crevices of crucibles of
blast furnaces, may be signalized as a particular variety of silica.
M. Rose having examined some specimens, remarks that they
all disengaged traces of ammonia when fused with caustic
potash, whilst they disengaged nothing by simple calcination.
This fact proves that this silica contains a little nitruret of silicium,
and indicates that it must have been formed by the combustion
of silica mixed with some of the nitruret. According to this it
was very unlikely that it belonged to the crystalline variety. In
fact M. Rose found its density only equal to 1-842 ; though it is
true that this determination was made onlv upon a very small
mass.
D2
36 Prof. H. Rose on the different States of Silicic Acid,
Thus, en resume, we are obliged to admit the existence of two
distinct moditications of silica, — one amorphous, the density of
which varies from 2 '2 to 2"3 ; the other crystallized, the density
of which is 2"6. This last is formed in the humid way alone,
or at least in presence of water ; the first is produced either in
the humid way or by fusion. Crystallized silica is the only
kind found in granite.
It is impossible not to be struck with the importance of these
facts for the discussion of the theories proposed to account for
the origin of granites. Accordingly the author treats this im-
portant question in detail.
It is known that the theory of Werner on the Neptunian
origin of granite was afterwards completely abandoned by geo-
logists, and replaced by the Plutonic theorj'. The latter, however,
has always met with adversaries, especially among chemists, and
seems to have been shaken more and more during the last few
years. MM. Fuchs, G. Bischoff, and more recently M. Delesse,
particularly deserve to be mentioned as having most contributed
to raise doubts as to the tenability of this theory.
Fuchs especially bases his objections upon the simultaneous
presence in granite of minerals the points of fusion of which are
extremely different, and upon their reciprocal penetration, which
does not permit one to doubt their simultaneous formation. He
attributes also considerable weight to the absence, in granite and
analogous rocks, of xitreous matter which ought to be found in
the productions of an igneous fusion.
Bischoff was in like manner led to reject the hypothesis of the
igneous origin of granite by the fact that in this rock felspar, an
element rather fusible, is generally encrusted in mineral quartz,
almost infusible ; the felspar, consequently, solidified first, which
is inexplicable on the hypothesis of a crystallization produced by
the cooling of a melted mass. But he forms his opinion also on
the considerations drawn from the study of all the elements of
granite.
One of the elements of granite, felspar, can be artificially ob-
tained either in the humid or dry way. Daubree has succeeded in
producing a crystallized felspar similar to that of the trachytes by
the action of water on obsidian or clay in the presence of an alkali,
under the influence of a high temperature and great pressure.
With respect to its production by means of ignition, it was
accidentally observed in the remains of a copper furnace at
Sangershausen, but we have not yet succeeded in obtaining it at
will ; by the fusion of felspar or its elements and by a slow cool-
ing, only vitreous matters have been obtained. This formation
of felspar is therefore possible, but it seems to require a com-
bination of circumstances difficult to realize.
and un the Origin of Granites. 37
The numerous pseudomorphous felspars in the forms of anal-
cime and Laumonite^ described by Scacchi, Haidinger, Bischoff,
and Rammelsberg, prove moreover that this mineral is easily
formed in nature in the humid way.
Mica can also be produced in both ways. The pseudomor-
phous micas, in the forms of scapolite, felspar, and Andalusite,
show the possibility of its formation under the influence of water.
On the other hand, its presence in the lava of Vesuvius proves
that it can also be formed in the igneous way. But there seems
to be an essential difference in the composition of mica, corre-
sponding to these two opposite origins.
Most of the micas, and particularly that of granite, contain
small quantities of water and fluorine which are dissipated by
calcination, so that the crystals become opake and lose their
brightness. On the contrary this does not occur with the vol-
canic micas, which contain neither water nor fluorine. This
observation seems to establish the fact that the mica of granites
must have been formed under the influence of water, and not of
heat.
But it is the examination of the quartzose elements which
especially forces us to reject the hypothesis of the igneous origin
of granite. It is recognized that quartz in granite generally
moulds itself on crystals of felspar, and consequently has crystal-
lized last of all, which fact is inexplicable on the hypothesis of a
previous fusion. The attempt has been made to reply to this
objection, by supposing that fused quartz might remain liquid
at a temperature inferior to its point of fusion ; hence the theory
of surfusion of M. Fournet. But, as M. Durocher remarked,
the phsenomeua of surfusion are manifested only between very
narrow limits of temperature, whilst it must here be admitted
that the quartz had preserved its liquidity at least a thousand
degrees below its point of fusion, which appears inadmissible.
The quartz of veins often contain water or other volatile
liquids, hydrated oxide of iron, carbonate of iron, and other
minerals decomposable by heat, which facts, as M. de Senarmont
justly remarked, evidently prove its aqueous origin. With re-
spect to the quartz of granites, it is often found in the form of
smoky quartz, its colour arising from a volatile or combustible sub-
stance, probably carbonaceous, which is expelled by calcination.
It is impossible to explain the separation, in a fusible mass, of a
very basic silicate, such as mica, from free silicic acid in the form of
quartz, which, at an elevated temperature, plays the part of an
energetic acid. Their formation in the humid way implies, on
the contrary, nothing contradictory; for we know that at a low
temperature silica scarcely plays the part of an acid, carbonic
acid and even water surpassing it in energy in this respect.
38 Prof. II. Rose on the different States uf Silicic Acid.
The remarkable purity of the quartz of granites is also in op-
position to this theory, which would make of this element, in a
state of surfusion, a mother-liquor from which the other cry-
stallized minerals of granites had by degrees separated them-
selves.
If the external appearance of granites is not that of a fused
mass which has ciystallized by slow cooling, like that of devitri-
fied glass, neither have we ever succeeded in producing, by the
slow cooling of a mass of fused granite, a mass of crystalline
structure. In this manner vitreous masses similar to obsidian
have alone been obtained.
The author mentions on this subject an interesting experi-
ment by his brother, M. G. Rose. When a granite rich in
quartz is subjected to fusion, felspar and mica fuse and gradu-
ally dissolve a part of the quartz, but a portion of the latter
remains in the form of grains or nuclei in the middle of the
vitreous mass. A granite very rich in quartz, from AYarmbrunn
in Silesia, having been subjected to the heat of a poi'celain fur-
nace, was transformed in this manner into a mass of obsidian, stiU
containing \\hite nuclei of quartz. These nuclei were carefully
separated from the obsidian, when they were found to be formed
of amorphous sihca, whose density was from 2"3-i to .2'35, and
which was acted on by hydrofluoric acid with the energy peculiar
to this variety.
Lastly, M. Rose regards as a strong objection against the
igneous origin of granite, the presence of minerals, such as
Gadolinite, Allanite, &:c., which at a temperatui'e more or less
elevated, suddenly present the phfenomenon of incandescence, at
the end of which they experience a permanent modification of
their properties, and become less capable, or even incapable of
being acted upon by acids. These minerals are found exclusively
in granite rocks ; and their presence proves that these rocks have
not been exposed to a temperature sufficient to determine their
metamorphosis, which nevertheless generally requires only a dark
red heat.
M. Scheerer having remarked in some of these minerals an
increase of density after their ignition, endeavoured to explain
their presence in granite rocks, to which he attributes an
igneous origin, by supposing that during the very slow cooling
of these rocks, giving rise to a contraction to which the mass
did not completely yield, the elements of these minerals assumed
a peculiar state of separation and tension. This explanation
falls before the fact verified by M. Rose, that all these minerals
do not present this increase of density ; samarskife, for example,
has a less density after its ignition. In order to meet the ob-
jection which geologists might raise, that pressure might oppose
Dr. Woods on a New Actinometer. 3'J
the metamorphosis of these minerals in granite, the author en-
deavoured to heat them in closed glass tubes full of air, the
expansion of the air by the heat giving rise in this case to a con-
siderable pressure. He proved that incandescence took place
quite as well in this case — in fact, that it was even facilitated by
])ressure.
One might, it is true, suppose that these minerals, especially
(ladolinite, were formed at the same time as the granite and by
fusion, but that afterwards, under the prolonged intluenee of
the atmosphere, water, an elevated temperature and perhaps
other causes, they had undergone a metamorphosis accompanied
by a fixation of caloric, and that thus they had passed into another,
isomeric state in which they are capable of disengaging their
latent heat by calcination and of presenting the phsenomenon of
incandescence.
Prof. Rose observes that this hypothesis contains nothing con-
trary to the views which he advances. Certainly no one imagines
that the elements of granite have been in a complete state of
aqueous solution, from which, by degrees, they have been sepa-
rated by crystallization. It is possible that these elements
})roceed from an anterior rock which had an igneous origin,
and which had assumed the crystalline state under the in-
fluence of water, heat, and pressure, as in the experiments by
which M. Daubree succeeded in obtaining several crystallized
minerals. A similar hypothesis has often been published, par-
ticularly by Mr. Sterry Hunt. It has the advantage of explain-
ing the absence of organic remains in granite, although this rock
might have been formed after the appearance of organized beings.
It is clear that these observations apply, not only to granites,
but to all crystalline rocks containing quartz, especially to
quartzose porphyries and trachytes. The hypothesis of the
igneous origin of these rocks is incompatible with the actual
state of our chemical knowledge.
VII. Di'scription of n neiv Actinnineter.
By Thomas Woods, M.D*
PROFESSOR DRAPER, of New York, published a paper in
this Magazine for September 1857, in which he showed that
a solution of peroxalatc of iron is decomposed by light, protox-
alate of iron being formed with evolution of carbonic acid —
Fe^ 0^ 3C^O"' = 2reO, C^O-V 200^.
In order to tind the amount of actinism which had caused the
change, the quantity of protoxalate produced, or of the carbonic
* l.'oiuimiiiicated bv the Autlior.
40 Dr. Woods on a New Actinometer.
acid which had been given oif, was to be measured : but herein
lay the difficulty ; it was required to find the amount of gold
precipitated from its chloride by the proto-salt in the solution of
peroxalate which had been exposed to the light, or to mea-
sure by weight or volume the carbonic acid which had been
evolved during the same exposm-e. Now, as Mr. H. C. Draper
says in a paper published in the Photographic Journal for last
September, "even an enthusiast would soon tire of daily following
out these details." Indeed the labour would be too great, even
if the results were rigidly exact. The latter gentleman, Mr.
H. C. Draper, suggests the weighing of the apparatus in which
the peroxalate is exposed, both before and after the exposure,
taking the precaution to expel the dissolved carbonic acid by
means of a stream of hydrogen, and thus to find the amount of
fixed air generated by the loss of weight the apparatus sustains.
This idea is ingenious ; but the process would be very little if at
all less troublesome than the others.
An easy and expeditious plan for the measurement of the
actinic efi'ect of light is a gi-eat desideratum. It would relieve
the art of photography of half its failures, and would be of still
greater advantage to its science. In order to give a helping
hand towards its attainment, I have endeavoured to render the
use of the peroxalate of iron as a photometric agent, both ma-
nageable and simple.
If after exposure any process is required to define the quantity
of change effected by the light, especially any process involving
knowledge of chemistry or nicety of manipulation, no doubt it
will be neglected, except perhaps by the few "en- Fig. 1.
thusiasts," whose results would therefore be of limited
value. For this reason I have endeavoured to find a
method of measuiing the photometric changes at
once, and by the eye only, in the following manner : —
having nearly filled a phial with a solution of peroxa-
late of iron, I passed through its cork a glass tube
into the bottle, both tube and cork fitting air-tight in
their places. This tube, open at both ends, dipped by
one of them under the surface of the solution, so
that when the bottle was exposed to light, any car-
bonic acid evolved should collect over the fluid,
pressing it into the tube ; and a scale applied to the
latter would show" at once the amount of action going
on. A reference to fig. 1 will explain the construc-
tion of the Actinometer. A is a low- sized square
phial, capable of holding about two ounces. B is the
tube passing through the cork into the solution of
peroxalate of iron. The carbonic acid collects in the space over
i C
Dr. Woods on a New Aciinometer.
41
the solution, and the fluid is raised correspondingly in the tube,
and read oflF on the scale C.
This is the principle of the actinometer ; and for taking an
occasional observation the above answers pretty well ; but there
are other circumstances to be taken into account in the construc-
tion of a more perfect instrument. For instance, if the tempera-
ture varies, the indications are interfered with, and that to an
extent the greater the more sensitive the apparatus is. For it is
obvious that the sensibility of the actinometer may be carried
to any extent by making the tube proportion- Fig- -•
ally small in the bore ; but then for the same
reason any change of temperature will corre-
spondingly affect the rising of the fluid. There-
fore for accurate measurements it will be neces-
sary to have a thermometer dipping into the
solution, and a preliminary experiment made in
order to find to what extent the change of
temperature affects the instrument. It will
also be convenient to have a second tube pass-
ing through the cork, but not into the fluid,
closed of course by a cork or stopcock when
the instrument is in use. This tube is for
the purpose of allowang the carbonic acid to
escape when desirable, or for filling the vessel
or emptying it when the solution is exhausted
of peroxalate. The apparatus I would there-
fore recommend, and which I have tried (only,
however, for a few days) with apparent success
in determining the actinic action of light, may
be seen in fig 2. It shows half the real size of
the instrument 1 used.
A is the phial, B the tube dipping under
the surface of the solution. C a thermometer,
also dipping into the solution, whose graduated
scale serves too as a scale for reading off the
height to which the fluid ascends in the tube.
D is the smaller glass tube passing through the
cork, but not into the solution. When the
fluid is raised nearly to the top of the tube
B by the pressure of the carbonic acid, it may
be drawn down again and set to any mark
by opening partially the tube D until suffi-
cient fixed air escapes to allow it to descend.
m
I give in the following page a representation of tlie heights
to which the fluid rose during different parts of two days.
42
Dr. AVoods on a Neiv Actinometer.
Height to
which fluid
rose in tube
Hour of observina
h m
8 A.M. Dec.
4 50
4 15
3 45
3 35
1 30
1 25
5 S
to
&
S B
5 S
2|
Height to
which fluid
rose in tube J
Hour of obsening.
SCO
« 23 i;
- I'M
s s
S S
- 7
A.M. Dec. 9, ^ S
when shaken. •= -g
3 45
3 30
3 15
3
2 45
2 30
2 15
12
11
43
11
30
11
15
j; -a
'7- «
jT S
I £
10 30
_
10 15
—
10
9 43
n
9 30
_
9 A.M. Dec. 6
Dr. Woods on a New Actinometer, 43
The marks indicate the successive heights of the fluid at the
diflPerent hours mentioned. The cock D was turned two or three
times to allow the fluid to descend, as otherwise it would have
overrun the tube.
The thermometer is not registered in these trials, as the tem-
perature did not vary more than one or two degrees. The acti-
nometer was at a closed window ; the weather was dull and rainy,
except occasionally, as at 12 o'clock December 7th, and 2 o'clock
December 8th. In the sunshine, in the open air, the rise of the
fluid was about three times as great as the largest space in the
same period of time. The bore of the tube I used was ^th of an
inch in diameter, and the solution in the bottle exposed a surface
of about three square inches. I mention these particulars, as
on them depends the sensibility of the instrument. The larger
the surface of fluid exposed, of course the greater will be the
action of the light ; and the smaller the bore of the tube the
greater will be the rise for a given evolution of carbonic acid. I
tried a thermometer tube of about -\jth of an inch in diameter,
and the fluid rose rapidly, perhaps a couple of inches in a minute,
but in jerks and in-egularly ; and I cannot yet say how far the
bore may be diminished with utility.
When the fluid is first exposed it shows no evolution of car-
bonic acid, although the action of the light produces it. The
gas is dissolved, to a certain extent, in the fluid, and until the
latter is saturated no rise in the tube occurs. The point of
saturation is reached after a greater or less time, according to
the light, generally in about fifteen minutes. This is only a
small inconvenience ; and I got rid even of this loss of time by
having a slight excess of oxalic acid in the fluid, and by adding
a couple of grains of carbonate of potash, so that saturation was
at once accomplished. But there is a more serious annoyance ;
the fluid having been saturated with the carbonic acid, gives it
out again even in the dark, so that luitil it all nearly disappears
the fluid continues to rise ; the removal, therefore, of the actino-
meter from the light does not immediately stop the rising. This
would not aff'ect the indications if the height of the fluid in the
tube was marked immediately before removing it ; but there is a
danger that the carbonic acid of saturation may be partially
escaping into the space above the fluid, even during the conti-
nuance of an observation, so that we may have two sources of
evolution, one the action of the actinism at the moment, and the
other the saturated state of the fluid. For instance, if a strong
light fell on the instruuient, the gas would be generated quickly ;
if the light then diminished, the carbonic acid which would then
be given out, might be due both to the action of the diminished
liiiht and to the saturated stale of the fluul. 1 cannot say
44 Dr. Woods on a New Actinometer .
positively whether such a double action does take place ; it ap-
pears probable ; but it might be, that as long as the light con-
tinues to fall on the solution, the saturated state is kept up, and
consequently none comes oflf, except what is at the moment pro-
duced. This point will require some trials to decide. The extent
to which the rise occurs is, however, not great, as may be seen
by referring to p. 42, and might have been due in this case to
an accidental circumstance.
If I had time to make experiments with this instrument, I
would not publish this account of it, as the doubts I have ex-
pressed might be solved, and more certain results might also be
obtained by using tubes of various diameters, until the most
proper for all purposes would be found : but I have done all I
expect to do for an uncertain period ; I thei-efore give the de-
scription of the actinometer as it is, and for what it is worth, to
the scientific world, believing it to be at least the germ of a
useful and interesting instrument. It may be of use to the
photographer as a means of exactly measuring the time of expo-
sure of a sensitive plate. The period of time, as reckoned by
seconds, will not always give the same amount of actinic force,
as the light may vary considerably between two experiments, and
yet not affect the eye. If, however, a good picture be obtained
during the i-ise of, say two degrees on the actinometer, the same
amount of actinism must always be present during the same rise,
be the time of rising longer or shorter. To science also it ought
to be a valuable help if its indications are sufficiently reliable.
I should have mentioned that the strength of the solution of
peroxalate of iron I employed was 35 grains to the ounce of
water ; but I believe this strength might be advantageously in-
creased. It will also be necessary, for comparative experiments,
to have a cover for the actinometer, in which an aperture is cut
of a certain size, say one or two square inches, in order that a
known extent of surface may be always acted on. The tube will
also require to be covered in delicate experiments, as the light
acts on the fluid in it, as well as on that in the bottle.
I must advise those persons who adopt the rough and ready
method of manipulating, that in making this apparatus, simple
as it may appear, there is great caution to be observed in causing
the stopper of the bottle to be air-tight, and also the apertures
through which the tubes and thermometer pass. When the fluid
rises in the tube, a great pressure is sustained by the interior
of the phial; and if this be not thoroughly provided against,
the air will find some small hole, too minute for observation, by
which, very gradually, almost insensibly, to escape ; and so the
results would be vitiated,
Parsonstown, Dec. 10, 18.5!).
Dr. Woods on a New Actinometer. 45
P.S, Since the above was written I have made some experi-
ments with the actinometer, and it has answered ray expectations.
I believe it is a rehable register of the amount of action of light.
The most important precaution to be taken in its use is to guard
against change of temperature, or to have a previous knowledge
of the extent to which the change will aflfect the instrument.
Increase of temperature seems to act on it in three different
ways. It expands the liquid and confined air, causing the liquid
to rise in proportion to the relative bulk of the vessel and tube,
as in a thermometer. It expels the carbonic acid from the satu-
rated solution in addition to that produced by the light : the
amount of carbonic acid a fluid can dissolve depends on the tem-
perature ; the higher the latter, the less gas the fluid can con-
tain ; so that if during a lengthened observation the tempera-
ture increases, carbonic acid is expelled independent of actinic
action. And thirdly, the higher the stationary temperature is,
the greater seems to be the power of the light. In this, as in
all chemical processes, heat increases the action. For instance,
during a day's exposui-e, when the thermometer was at 36° F.,
the fluid of the actinometer rose about 3 inches, whereas in
the same period of time, when the thermometer was at 60° F., it
rose about three times as high. Whether this increase w^as alto-
gether due to the light acting more energetically on the warmer
fluid, or partly to the higher temperature expelling some carbonic
acid, I cannot at present decide.
I have used a solution of peroxalate of iron, 35 grains to the
ounce ; and as it may facilitate matters for others who may wish
to try the instrument, I will describe in detail how I obtained
the solution.
I dissolved in 6 oz. of water 1043 grs. of protosulphate of
iron; I added 180 grs. of sulphuric acid of 1*84 spec, grav., and
boiled; while boiling I threw in 140 grs. of nitric acid of 1-42
spec. grav. This caused an effervescence of nitrous acid, for which
the operator should be prepared by having the vessel of sufficient
capacity and under a flue. The protosalt was thus converted into
the persalt. Red prussiate of potash should now produce no
blue colour. I then precipitated the peroxide of iron with am-
monia and washed with warm water. I had thus 300 grs. of
anhydrous peroxide of iron ; I diffused this in 20 oz. of water,
and added 720 grs. of crystallized oxalic acid — an excess of
about 10 grs. of acid. This dissolved the iron and gave me a
solution of 712 grs. of the peroxalate — about 35 grs. to the ounce.
The bottle of the actinometer holds about 2 ounces, and I used
this quantity of fluid without renewing it for some weeks. How
long it may retain its power I cannot say.
Pftrsonstown, Doreniher '2?i. 18.'39.
[ -IG ]
VIII. On the possibility of finding a Root, real or imaginary, of
every Equation. By Professor Challis*.
AS the proof of the proposition that ever)' equation has a
root is at this time attracting the attention of mathema-
ticians, I am desirous of adding a few considerations to those
contained in two articles on this subject, which 1 communicated
to the Numbers of the Philosophical Magazine for February and
April 1859.
1. The proposition belongs to a branch of pure calculation,
which is antecedent to, and altogether independent of, the rela-
tions of space ; and consequently the proof of it does not neces-
sarily involve the consideration of either lines or angles. The
use that has been made of geometiy of two and of three dimen-
sions in proofs that have been recently proposed, can only be
regarded as an auxiliary means of exhibiting the variations of
the value of a function corresponding to variations of its vari-
ables, and not by any means as essential to the demonstration
of the proposition.
2. In all the proofs that I am acquainted with, as in that
which I have given in the articles above referred to, the unknown
quantity x is assumed to be represented by a function of the
form z-\-y V — 1, z and y being real quantities, positive or ne-
gative. The reasons for this assumption, which are not usually
much dwelt upon, appear to be such as follow. An equation
may always be supposed to be formed according to the conditions
of a proposed question ; and its object is to discover some un-
known quantity which is the ansv/er to the question. In the
formation of the equation, the unknown quantity is brought into
relation with certain known quantities by operations conducted
in accordance with the given conditions, and by algebraic rules.
The operations are necessarily algebraic, because the relative
magnitudes of the given quantities and the quantity sought for
are unknown ; and it is the essential princi])le of abstract algebra
to furnish rules and symbols of operation which are proper for
calculating indej)endently of the knowledge of relative magni-
tudes. On account of this necessary generality in algebraic
operations, the final equation involves conditions not contained
in the proposed question, and its dimensions are determined
accordingly. When the equation is formed, the unknown quan-
tity becomes an algebraic function of the given quantities, the
exact form of which in certain cases may be actually found. In
all other cases such a function can be obtained in the form of a
series, by the following, or some equivalent method.
Let the equation be of five dimensions ; and if any terms be
* Communicatetl bv the Author.
On the Proposition that every Equation has a Boot. 47
wanting, let it be transformed, by adding a given quantity to its
roots, into an equation in which no coefficient is zero, as "
or' +px'^ -\-qxr^ + r.v^ + sx -i-t = 0.
Then supposing that .v = Af~{-'Bt^ + Ci^+ &c., it may be readily
shown by the method of the reversion of series, that
t rt^ t^
If it be supposed that x = a -\- bs + cs^ + d^ + &c., the same method
gives, b, c, d, &c. by means of simple equations as functions of
a ; but a itself is given by the equation
a^ +pa'^ + qa^ + ra^ + / = 0.
Fx'om this equation a value of a may be obtained by the j)rocess
just indicated, and thus x will be expressed in a series proceed-
ing according to the powers of s. Similar reasoning applies to
the other coeJSicients.
These different series for x might be pro])er for finding real
roots of equations ; but as they are not necessarily convergent,
they do not prove that a root can always be found. They show,
however, that x is an uUjehraic function of the coefficients; and
as every algebraic function reduced to numbers is of the form
r + y v^ — 1, it may consequently be assumed that x is of that
form.
3. Hence z-\-]j v^ — 1 may be substituted for x in the given
equation /(a?) = 0 ; and as after this substitution it does not cease
to be an equation, we shall have
or
P-fQv/-l=0,
P and Q being veal functions of z and //. I am aware that ma-
thematicians who have given especial attention to this question,
have not thought themselves at liberty, after substituting
r + y y' — \ for X, to equate the result to zero, but have endea-
voured to prove by independent considerations tluit there are
values of z and y which will make P and Q vanish simulta-
neously. I confess that I am unable to see the necessity for
this course of reasoning, which has the disadvantage of requiring
a peculiar and complicated analysis, of the validity of which it is
difficult to judge. It being once admitted, on the grounds
above indicated, that the unknown quantity of an equation may
have the form z-\-y v^ — 1, it must surely be also admitted that
this expression may be put in the place of .r without destroying
the equation. According to the view that I take, the resulting
48 M. Hlasiwetz on Quercitrine.
equation P + Q v^ — 1 = 0, being equivalent to P = 0 and Q = 0,
proves that there are values of z and y which make P and Q
vanish simultaneously ; and it only remains to show that they
can be found, which may be simply done as follows. Prom the
equations P = 0 and Q = 0, one of the unknown quantities z and
y may be eliminated by a direct process ; and as it has a real
value, the resulting equation has a real root. Consequently, the
original equation being given with numerical coefficients, this
root and the corresponding value of the other unknown quantity
may be found by approximate methods. Thus the possibility of
finding a root, real or imaginaiy, of any proposed numerical
equation is demonstrated.
Cambridge Observator\',
December 21, 1859.'
IX. Chemical Notices from Foreign Journals, ^y E. Atkixsox,
Ph.D.,F.C.S., Teacher of Physical Science in Cheltenham College.
[Continued from vol. xviii. p. 459.]
QUERCITRINE, the colouring matter first discovered by
Chevreul in quercitron bark, has since been found to be
contained in a great number of plants of difi'erent orders ; among
others Rochleder has found it in the horse-chestnut. Rigaud
found that it belonged to the class of glucosides, and was capable
of being decomposed into grape-sugar and quercetine.
C58H3oo34^HO = C'2Hi5 0i^ + C''6Hico-2o.
Quercitrine. Glucose. Quercetine.
Hlasiwetz* has now found that quercetine itself can be re-
solved into two substances, one of which is a saccharoid matter,
and the other is a weak acid. Quercetine is boiled with a
concentrated solution of potash for some time, the mass then
diluted with water, and filtered off" from a flocculent substance
which forms, the nature of which from its small quantity could
not be determined. The solution is then evaporated to dryness,
extracted with alcohol, the alcoholic solution distilled off, and
the residue dis.solved in water. To the solution, sugar of lead is
added, which causes a copious precipitate.
The solution filtered off from the lead precipitate, and evapo-
rated, deposited after some time crystals which, by analysis and
from their properties, were identified with phloroglucine, the
saccharoid substance formed as a product of decomposition of
phloretine t-
The precipitate produced as above by acetate of lead is mixed
* Liebig's Annahn, October 1859. f Phil. Mag. vol. xi. p. 203.
M. Rochleder on Fraxeiine. 49
with water and decomposod by sulphuretted hydrogen, and the
licpiid filtered from the sulphide of lead formed. 'J'his filtrate
yielded, on careful evaporation, a substance crystallizing in fine
silky needles, which possessed a feebly acid reaction, and in
appearance and properties greatly resembled gallic acid. This
substance Hlasiwetz has named quercelic acid. Its most cha-
racteristic property is its relation to oxygen. When a drop of
alkali is added to a very dilute solution of the acid, it imme-
diately turns yellow, and when agitated in the air gradually
becomes of a brilliant red. The formula of the acid was found
to be C34 Hi^ Oi«.
From its general resemblance in appearance and properties it
appears to stand closest to ellagic acid, with which it is homo-
logous.
C34H12 01G . . Quercetic acid
C^^ H« 0'« . . Ellagic acid
If this be the formula of quercetic acid, that of quercetine
must be altered. Hlasiwetz considers that it has the formula
(;;4« f J 16 Q2o^ and expresses its decomposition by the following-
equation : —
C46Hi6 020 4-2HO = Ci2 II«0« + C34 H^^ 0^^.
Quercetine. Phloroglucine. Quercetic acid.
Hence the original formula for quercitrine must be altered.
Quercitrine contains the elements of sugar, of phloroglucine, and
of quercetic acid.
C70H3(5 04o=, c>Ml« 0« ^-6H0.
Quercitrine. C^'* II ^ - 0 '^ J
This formula would require that quercitrine should yield in its
decomposition 46'3 per cent, sugar. Rigaud found 41-9 per
cent. Other experiments, however, by Hlasiwetz and by Roch-
leder, with specimens of various preparation, yielded quantities
of sugar which correspond to 1 and to 3 equivalents of sugar.
It seems therefore probable that different kinds of quercitrine
may exist containing different proportions of sugar, analogous
consequently to the natural oils and fats with their varying
quantities of fatty acids.
Rochleder * analysed a specimen of fraxetine crystallized several
times from alcohol, and obtained numbers which he expresses
by the relation C**'Mr^^O-". But the numbers found by Roch-
leder agree better, as Wurtz suggests -f, with the formula
* I'oggeudorrt's Annalen, May 1851).
t Repertoire de C/timie, September 185f).
Phil, May. S. 4. \o\. 19. No. 12 1. Jan. 18G0. E
50 M. Hlasiwetz on Chinovic Acid.
Q42fi22 02G, Trcutcd witli dilute sulphuric acid, fraxine is re-
solved into grape-sugar and fraxetine, C^° li^^ 0^^. Adopting
Wurtz's formula for fraxine, its decomposition may be thus ex-
pressed : —
C42H22O26-f2HO = C12H'2O'2_,_C30H12O^^
Fraxine. Glucose. Fraxetine.
Fraxetine has an astringent taste. It is difficultly soluble in
cold and in hot water : its aqueous solution has a feebly acid
reaction. In its properties and formula it appears allied to escu-
letine, C^SHi^ois, and quercetic acid, C^^yisQis^
Phloroglucine, as Wurtz points out, has the composition of
phenylglycerine, the triatomic alcohol corresponding to phenylic
alcohol, just as glycerine corresponds to propylic alcohol.
C^H^O^ Propylic alcohol C^^H^O^ Phenyhc alcohol.
Q6 H8 04 Pi-opylic glycol C^^ JJ6 04 Pheuylglycol (pyrocatechine).
C^H^OS Glycerine Ci^H^QS Pheuylglycerine
Hlasiwetz* has published the result of some researches by
himself and Von Gilm on chinovine, a bitter principle, supposed
to be an alkaloid, extracted from C/mia nova. These investiga-
tions have shown that it belongs to the class of glucosides.
Chinovine was dissolved in alcohol, and the solution saturated
with hydrochloric acid gas. The liquid soon became heated,
and deposited a crystalline powder which was purified by re-
crystallization from alcohol, in which it is difficultly soluble.
Chinovic acid,ixs Hlasiwetz names this substance, forms when pure
a brilliant white, crystalline powder ; it is distinguished by its
insolubility, its best solvent being boiling alcohol. Its solutions
are very bitter. The alkaline chinovates are formed on the
addition of the alkalies to a solution of the acid, as voluminous
gelatinous precipitates. The salts of the alkaline earths are
similar. Chinovic acid has the formula C^^ H^^ 0^, and is bi-
basic ; it is a weak but very permanent acid. It is not attacked
by hydrochloric or by boiling nitric acid. Sulphuric acid dis-
solves it, and deposits it unchanged on the addition of water.
When distilled, odoriferous vapours are evolved, which condense
to a thick, amber-yellow, resinous liquid. In its properties chi-
novic acid agrees most closely with Hofmann^s insolinic acid,
C^^H^O^, and moreover, from its formula, C'^^H^^O^, it is
homologous with it.
The acid alcoholic solution from which chinovic acid has been
filtered, contains a saccharoid substance, which has the formula
C- H'^ 0'^. It appears to be identical with maunitane f a sub-
* Liebipj's Annalen, August 1859.
t Phil. Mag. vol, xii. p. 536.
M.Vhth on Ericinone. 51
stance formerly regarded as anhydrous mannite. The resolution
of chinovic acid might therefore be thus expressed : —
Chiuovine. Chinovic acid. Manuitane.
Athamantine, a crystalline substance found by AYinckler in the
seeds of Athamanta oreoselinum, is decomposed by hydrochloric
acid into valerianic acid and oreoseloue. Winckler and Schne-
dermann assigned to it the formula C^"* H'^ 0'' :
Athamantine. Valerianic acid. Oreoselone.
Gerhardt doubled its formula, and therewith the formula of
oreoselone. Geyger has recently made some analyses which lead
to the same formula ; and the analysis of the nitro-compound,
Q48 j^27 (N0'*)^0^^ an amorphous substance prepared by adding
athamantine to cold fuming nitric acidj confirmed Gerhardt's
view. By the action of chlorine on athamantine, a yellow resi-
nous substance is formed, which has the formula C"*^ H^^ CIO'*.
In an investigation of Kino, Eissfeldt was led to the conclusion
that all plants whose aqueous extracts give a green colour with
solutions of ferrous salts, yield 'pyrocatechine when submitted to
dry distillation, and that all plants which give a blue or bluish-
black precipitate with ferrous salts yield pyrogallic acid by that
treatment. Eissfeldt also established the formula of pyrocatechine,
which differs from that of pyrogallic acid by containing less
oxygen : —
Pyrocatechine. PjTogallic acid.
Uloth* has investigated the plant of the bilberry, and several
allied plants which are distinguished by containing a large quan-.
tity of a substance which turns iron solutions green, and has con-
firmed the truth of Eissfeldt^s generalization. All the plants which
Uloth examined belong to the natural order of the Ericincje, and
were all found to contain, besides pyrocatechine, a crystallizable
indifferent substance which he calls Ericinone. It was obtained
as follows : — After the ])yrocatechine had been precipitated from
the aqueous extract of the plant by sugar of lead, the filtrate was
saturated with sulphuretted hydrogen, the sulphide of lead filtered
off, and the filtrate evaporated to dryness. On subjecting the
mass to dry distillation, the ericinone sublimed over and con-
densed to white silky needles, which under the microscope are
seen to consist of quadratic prisms.
It is a neutral substance, but its aqueous solution gradually
decomposes, assuming an acid reaction. Even the crystals decom-
* Liebig's Annalen, August 1859.
E2
52 Boyal Society : —
pose when exposed to the air. It melts at 167°, and is thus distin-
guished tVoni pyrocatechine. In its cheuiical rehitious it is indiffer-
ent ; it forms no combinations with metallic oxides, in which it
again differs from pyrocatechine. It reduces the oxides of the
noble metals with great facility, and is completely decomposed
by the alkalies. It is oxidized by nitric acid to oxalic acid, and
by the action of chlorine it is converted into chloranile, C'^ CI"* 0'*.
The analytical data lead to the formula C^'* Ri^ Qs. It differs
from pyrocatechine by containing more oxygen :
C24Hi2 09 = 2(C'2H6 0'*)+0.
X. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Contiuued from vol. xviii. p. 542.]
May 26, 18.59. — Sir Benjamin C. Brodic, Bart., Pre.?., in the Chair.
'TPIIE following communications were read : —
-■- "On the Intimate Structure, and the Distribution of the Blood-
vessels of the Human Lung." By A. T. II. Waters, Esq.
"On certain Sensory Organs in Insects, hitherto undescribed."
By J. Braxton Ilicks, M.D. Loud., F.L.S. &c.
" On Lesions of the Nervous System producing Diabetes." By
Frederick W. Pavy, M.D. Lond. &c.
The author commenced his paper bystating, that all the experiments
he had performed since his communication on the " Alleged Sugar-
forming Function of the Liver " had been placed in the possession
of the Royal Society, bad confirmed the conclusions he bad there
arrived at. As far as bis knowledge extended, it might be said that
in the healthy liver during life there is a substance which be bad
spoken of under the term of bepatine, and which possesses the che-
mical property of being most rapidly transformed into sugar when
in contact with nitrogenized animal materials. In the liver after
death this transformation takes jdace, but in the liver during life
there seems a force or a condition ca])able of overcoming the che-
mical tendency to a saccharine metamorphosis.
Experiments are mentioned to show that when the medulla oblon-
gata is destroyed, and the circulation is maintained by the performauce
of artificial respiration, the sugar formed in the liver as a jjost-
mortern occurrence is distributed through the system, and occasions
the secretion of urine possessing a strongly saccharine character.
Although the destruction of tlie medulla oblongataleads to this effect,
yet division of the spinal cord, which has been practised as high as
between the second and third cervical vertcbrre, has not been atteuded
with a similar residt. The brain (cerebrum) has also been separated
from the medulla oblongata by section through the crura cerebri, and
from the results of the experiments in which this operation has been
On Lesions of the Nervous System producing Diabetes. 53
performed, Dr. Pavy believed that tlie functions of the brain may be
completely destroyed, without placing the liver in the condition no-
ticeable after actual death, or after lesion of the medulla oblongata.
On account of the accidental disturbances, — such as implication of the
medulla oblongata, possibly by concussion, obstruction of the respi-
ration, and the effects of the great loss of blood sometimes attending
division of the crura cerebri, — the interpretation of the result is ren-
dered a little difficult. In an experiment, which proved most con-
clusive, performed to corroborate the author's previous observations
whilst his communication was being written, there were none of these
disturbing circumstances. In a healthy dog, during a period of diges-
tion, the crura cerebri were completely divided. The animal was
thereby thrown into a state of unconsciousness, but breathed efficiently
of its own accord. The urine in an hour and a quarter's time was
found perfectly free from sugar.
After poisoning by strychnine, the effect is the same as after de-
struction of the medulla oblongata. The circulation being maintained
by artificial respiration, the urine becomes strongly saccharine.
Looking to these facts, and to the effect of Bernard's puncture of
the fourth ventricle in producing diabetes, the author is led to regard
the medulla oblongata as a centre, either directly presiding over the
functional activity of the liver, or indirectly affecting it by altering
through the medium of another or other organs the condition of the
blood going to it ; and he has endeavoured to establish upon positive
grounds the channel by which the propagation of the nervous influ-
ence may take place. It was this line of research that conducted to
the discovery of the strongly diabetic effect produced by dividing
certain parts of the sympathetic.
The medulla oblongata being thus presumed to form a centre
giving to the liver a force which prevents the saccharine metamor-
l)hosis of its hepatine, experiment had already shown that it cannot be
through the spinal cord or the pneumogastrics separately, that the
transmission of nervous influence takes place. But an experiment was
j)erformed to determine the effect of dividing both the spinal cord and
the two pneumogastrics together. The cord was crushed between the
third and fourth cervical vertebrae, and about half an inch of each
j)neumogastric was cut away from the centre of the neck. Artificial
respiration was performed to keep up the circulation. The urine
remained entirely free from sugar, and the liver was found in an
cxsaccharine state at the moment of discontinuing the respiration,
and became strongly saccharine afterwards.
On next dividing all the nerves in the neck, an operation effected
by performing decapitation, the result that followed after three
(piarters of an hour's artificial resfjiration was strongly saccharine
urine. After this experiment, and that of division of the spinal cord and
])neumogastrics, reason was afforded for looking to the sympathetic;
and from the experiments that have been made and are described,
the following conclusions have been arrived at. The animal selected
for observation has been the dog, subsisting upon an animal diet, and
operated upon at a period of full digestion.
54 Royal Society : —
" Division, on both sides of the neck, of the ascending branches of
the superior thoracic gangUon which run up towards the canal
formed by the foramina in the transverse processes of the vertebrae,
for the vertebral artery, occasions an intensely marked diabetes. The
urine has been found most strongly saccharine within even half an
hour after the operation. The diabetic condition is only of a temporary
character, passing oif by the next day, and fatal pleurisy is always
induced.
" Division of the ascending branches of the superior thoracic
ganglion on one side of the neck only, has occasioned merely the
])resence of a trace of sugar in the urine in an hour and a half s time.
The same operation then performed on the other side has produced
in half an hour's time an intensely saccharine urine.
" Carefully ligaturing the two vertebral and the two carotid arte-
ries does not lead to saccharine urine ; but when the carotids have
been tied, and the tissue in connexion with the vertebrals before their
entrance into the canals is a little roughly treated, without however
dividing the larger sympathetic filament ascending from the superior
thoracic ganglion, the urine is rendered rapidly and strongly saccha-
rine.
" Division of the sympathetic filaments that have entered the
canals does not alone produce diabetes ; but if the contents of
these canals be divided, and the carotid arteries at the same time
ligatured, saccharine urine is the result.
" This result is produced when the contents of the osseous canals
are divided as high as the second cervical vertebra. It has also arisen
after destroying the structures in the neighbourhood of the vertebral
foramen on the posterior surface of the transverse process of the atlas,
but has not yet been noticed after a similar operation on the anterior
surface of the process.
" Dividing the contents of the canals and the tissue in immediate
contact with the carotid vessels has not produced diabetes ; but when
the carotids have been afterwards tied, strongly saccharine urine has
resulted.
" Of all the operations on the sympathetic of the dog that have yet
been performed, removal of the superior cervical ganglion the most
rapidly and strongly produces diabetes. After the removal of one
ganglion, the urine has been found intensely saccharine in an hour's
time, and the saccharine character has remained during the following
day, but has disappeared by the next. Subsequent removal of the
other ganglion a few days later has been followed in half an hour's
time with a strongly marked diabetic effect, which, however, has
been again only of a temporary nature.
" Division of the sympathetic in the chest has been several times
succeeded by saccharine urine. In one case after division on one
side only, the urine was intensely saccharine in half an hour's time.
On the other hand, many experiments have been made where both
sides have been operated on, and only a merely traceable, or in a
few instances, even no effect, has been noticeable.
"In the rabbit, removal of the superior cervical ganglia, when
On the Electrical Condition of the Egg of the Common Fowl. 55
the animal is in a strong and healthy state, is followed by diabetes;
but the effect is not so rapidly produced as in the dog. It has been
noticed at the end of four hours after the operation, and has been
observed to exist until the following day.
" Excision of the superior cervical ganglia in the rabbit with a
division of the pneumogastrics above their gangliform enlargement
close to their exit from the skull, has been attended with the produc-
tion of saccharine urine in a shorter space of time than when the
ganglia alone have been removed, notwithstanding that dinsion of
the pneumogastrics in the situation referred to, has not been seen by
itself to cause any positive effect."
Such is a simple statement of the principal conclusions derivable
from the author's experiments, which are given in detail in his com-
munication. As to the interpretation of the results that have been
obtained, this he leaves for further investigation, in which he is now
engaged, if possible, to disclose. The experiments on the sympathetic
were commenced under the notion that it might form the medium of
transmission of nervous force from the medulla oblongata to the liver.
From this supposition certain facts have been discovered which are
left for the present, without discussing whether the notion that led
to them is right or wrong.
"On the Electrical Condition of the Egg of the Common Fowl."
By John Davy, M.D., F.R.SS. L. & E. &c.
The structure of the egg suggested to the author the idea of its
exerting electrical action. This was confirmed on trial. Using a
delicate galvanometer and a suitable apparatus, on plunging one wire
into the white, and the other, insulated, except at the point of con-
tact, into the yolk, the needle was deflected to the extent of o° ; and
on changing the wires, the course of the needle was reversed. When
the white and yolk were taken out of the shell, the yolk immersed
in the white, the effects on trial were similar ; but not so when the
two were well-mixed ; then no distinct effect was perceptible.
Indications also of chemical action were obtained on substituting for
the galvanometer a mixture consisting of water, a little gelatinous
starch, and a small quantity of iodide of potassium, especially when
rendered very sensitive of change by the addition of a few drops of
muriatic acid. In the instance of newly-laid eggs, the iodine libe-
rated appeared at the pole connected with the white ; on the con-
trary, in that of eggs which had been kept some time, it api)eared at
the pole connected with the yolk, answering in both to the copper
in a single voltaic combination formed of copper and zinc.
The author, after describing the results obtained, declines specu-
lating on them at present, merely remarking, that in the ecouoniy of
the egg, and the changes to which it is subject, it can hardly be
doubted that electro-chemical action must perform an important
part, and that in the instance of the ovum generally, i. e. when com-
posed of a white and of a yolk, or of substances in contact, of hete-
rogeneous natures.
56 Royal Societtj : —
" On the Mode in wliich Sonorous Uiululalions are conducted from
the Membrana Tvnipani to the Labyrinth, in the Human Ear." By
Joseph Toynbcc, Esq., F.ll.S. &'C.
The opinion usually entertained by physiologists is that two
channels are requisite for the transmission of sonorous undulations
from the membrana tyrnpani to the labyrinth, viz. the air in the
tympanic cavity which transmits the undulations to the membrane
of the fenestra rotunda and the cochlea ; and secondly, the chain of
ossicles which conduct them to the vestibule.
This opinion is, however, far from being universally received ;
thus, one writer on the Physiology of Hearing contends that " the
integrity of one fenestra may suffice for the exercise of hearing*;"
another expresses his conviction that " the transmission of sound
cannot take place through the ossiculaf;" while Sir John Herschel,
in speaking of the ossicles, says " they are so far from being essential
to hearing, that when the tympanum is destroyed and the chain in
consequence hangs loose, deafness docs not follow J."
The object of this paper is to decide by experiment how far
tlie ossicles are requisite for the performance of the function of
hearing.
The subject is considered under two heads, viz. —
1. Whether sonorous undulations from the external meatus can
reach the labyrinth without having the ossicles for a medium.
2. Whether any peculiarity in the conformation of the chain of
ossicles precludes the passage of sonorous undulations through it,
1. Ca7i sonorous undulations reach the labyrinth from the
external meatus imthout the aid of the ossicles ?
This question has often been answered in the affirmative, appa-
rently because it has been ascertained that in cases where two bones
of the chain of ossicles have been removed by disease, the hearing
power is but slightlv diminished. In oi)position to this view, it
must, however, be remembered, that the absence of the stapes, or
even its fixed condition (anchylosis), is always followed by total or
nearly total deafness ; and the following experiments, which demon-
strate the great facility with which sonorous undulations pass from
the air to a solid body, indicate that the stapes, even when isolated
from the other bones of the chain, may still be a medium for the
transmission of sound.
Experiment 1.— Both ears having been closed, a piece of wood,
f) inches long and half an inch in diameter, was held between the
teeth, and a vibrating tuning-fork C having been brought within
the eighth of an inch of its free extremity, the sound was heard
distinctly, and it continued to be heard between five and six seconds.
Experiment 2. — One end of the ])icce of wood used in the pre-
vious experiment being pressed against the tragus of the outer ear, so
as to close the external meatus without compressing the air cou-
* Mr. Wharton Jones, Cyclopaedia of Surgerj', Art. " Diseases of the Ear,"
p. 23.
t Lancet, 1813, p. 3P0.
X Encyclopxdia Aletroj)olitana, Art. " Sound," p. 810.
Mr.Toj'nbeeori ike Mode oftransmission of Sonorous Undulations. 57
taincd within it, a vibrating tuning-ibrk C placed within a quarter
of an inch of its free extremity, was heard very distinctly at first,
and it did not cease to be heard for fifteen seconds.
Experiment 3. — Three portions of wood, of the same length and
thickness as that used in the previous experiments, were glued
together so as to form a triangle somewhat of the shape of the
stapes ; the base of this triangle being placed against the outer
surface of the tragus, as in the previous experiment, the tuning-fork
C vibrating within a quarter of an inch from its apex was heard for
twelve seconds.
Considering, as shown by the above experiments, the great facility
with which sonorous undulations ])ass from the air to a solid body, it
may, I think, be assumed that the undulations in the tym]ianic cavity
may be conveyed to the stapes even when this bone is isolated from
the rest of the chain, and conducted by it to the vestibule ; and
when it is also considered that the absence of all the ossicles, or even
a fixed condition of the stapes, is productive of deafness, there is
strong evidence in favour of the opinion that sounds from the
external meatus cannot reach the labyrinth toithout the medium of
the ossicles.
2. Is there ani/ peculiarity/ in the conformation of the chain ofossi-
cles which jJrecludes the passage of sonorous undulations through it ?
This question has also been answered in the affirmative, on account
of the various planes existing in the chain ; and secondly, on account of
the joints existing between the several bones composing this chain.
The following experiments refer to the influence of the varying
plane of the bones forming the chain, and of its articulations, on the
progress of sonorous undulations through it : —
I. Experiments illustrative of the influence of the variety of planes
in the chain.
Experiment 1. — Three pieces of wood, each 5 inches in length
/L
and half an inch thick, were glued together thus tX , so as to
represent the planes in which the malleus, incus, and stapes are
arranged in the chain of ossicles, while three similar portions were
glued end to end so as to form a straight rod, A watch was placed
in contact with one end of the straight rod, while the other was
pressed gently against the tragus so as to shut the external meatus.
The result was that the watch was heard nearly as distinctly as
when in contact with the ear. AVhen a similar experiment was per-
formed with the angular portion of wood representing the chain of
bones, the watch was also heard, but less distinctly than through the
straight portion.
Experiment 2. — A tuning-fork C, being made to vibrate, was
placed in contact with one extremity of the angular piece of wood,
the other being j)laced against the tragus of the ear ; and as soon as
the sound ceased to be heard, the straight portion was substituted,
when the tuning-fork was again heard, and it continued to be heard
for about three seconds.
58 Royal Society : —
Experiment 3. — A vibrating tuning-fork C was placed at one ex-
tremity of the angular piece of wood, the other extremity being held
between the teeth ; the fork was at first heard very distinctly, and
when its sound could no longer be distinguished, the straight piece
was substituted, and it was again heard for the space of two
seconds.
Experiment 4. — Instead of the horizontal portion of wood repre-
senting the stapes, three portions of the same size were made into
a triangle, and this was glued to the anterior surface of the inferior
extremity of the piece representing the incus, thus A ^. . The
previous experiment was then repeated with the substitution of this
apparatus for the angular one, and with nearly the same result, viz. '
the fork was heard through the straight piece about three seconds
after it had ceased to be heard by the apparatus representing the
chain of bones.
Experiment 5. — A piece of very thin paper was gummed over the
end of a glass tube 6 inches in diameter ; to the outer surface of
this paper was glued a model of the chain of ossicles similar to the
one used in the previous experiment ; a vibrating tuning-fork C
being placed in the interior of the tube and within a quarter of an
inch of the paper, the sound was heard through the free end of the
chain placed between the teeth for ten seconds ; when the sound
ceased to be heard, a straight piece of wood was substituted, and the
sound was not heard through it.
II. Experiments iUustrative of the infiuence of the articulations
in the chain.
Experiment 1. — Three pieces of wood, each about 5 inches
long and half an inch in thickness, were separated from each other
by pieces of india-rubber as thick as ordinary writing-paper, and they
were then fastened together so as to assume the angular form pos-
sessed by the chain of ossicles. The tuning-fork C being placed at the
free extremity of the chain, the other extremity being held between
the teeth, it was found that the sound was heard as distinctly and
for the same length of time, as when it passed through the chain
formed of three portions glued together.
Experiment 2. — When eight layers of the india-rubber were placed
between each piece of wood, there was still very little difference in
the intensity of the sound from that observed when it passed through
the portions glued together.
Experiment 3. — One, two, or three fingers having been placed
between the first and second pieces of wood, and eight layers of
india-rubber between the second and third, a very slight diminution
in the intensity and duration of the sound was observed as compared
with its passage through similar pieces when glued together.
Experiment 4. — The back of the hand was placed in contact with
the teeth, and the end of the vibrating fork C was pressed against
the palm ; the sound was heai'd very distinctly for several seconds ;
and when it ceased to be heard, a piece of solid wood 3 inches
On the Electrical Discharge of the Voltaic Battery. 59
long was substituted, through which the sound of the fork was again
heard faintly for four seconds.
The inference from the two series of experiments above detailed is,
that neither the variation of the plane existing in the chain of
ossicles, nor the presence of the articulations, is sufficient to prevent
the progress of sonorous undulations through this chain to the
vestibule.
The experiments and observations detailed above lead to the
following conclusions : —
1 . That the commonly received opinion in favour of the sonorous
undulations passing to the vestibule through the chain of ossicles is
correct.
2. That the stapes, when disconnected from the incus, can still
conduct sonorous undulations to the vestibule from the air.
3. So far as our present experience extends, it appears that in the
human ear sound always travels to the labyrinth through two media,
viz. through the air in the tympanic cavity to the cochlea, and through
one or more of the ossicles to the vestibule.
" On the Electrical Discharge in vacuo with an extended Series of
the Voltaic Battery." By John P. Gassiot, Esq., V.P.R.S.
In a recent communication, since ordered for publication in the
Philosophical Transactions, I described some exjieriments on the
electrical discharge in a vacuum obtained by the absorption of
carbonic acid with caustic potassa, and I showed that, when the dis-
charge from an induction coil was passed through such a vacuum, the
stratifications became altered in character and appearance as the
potassa was more or less heated. I have also in a former paper
(Phil. Trans. IS'fS, p. 1) shown that the stratified discharge can
be obtained from the electrical machine.
A description of an extended series of a water-battery was com-
municated by me as far back as December 1843 (Phil. Trans. 1844,
p. 39). This battery consists of 3520 insulated cells: some years
had elapsed since it was last charged, and I found the zincs were
very much oxidated ; on again charging it with rain-water, I ascer-
tained that there was sufficient tension to give a constant succession
of minute sparks between two copper discs attached to the terminals
of the battery, and placed about ith of an inch apart. On at-
taching the terminals of the battery to the wires in a carbonic acid
vacuum-tube inserted about 2 inches apart, I obtained a stratified
discharge similar to that from an induction coil.
The experiment was repeated with 400 series of Grove's nitric
acid battery. In this case distinct sparks between two copper discs
were obtained, and the luminous layers were shown in a peculiar and
striking manner, thus proving that the induction coil is not necessary
for the production of the striae, as in most of the experiments the
only interruption of the battery circuit was through the vacuum-
tube.
I had another tube prepared, substituting for metallic points balls
of gas-carbon. At first the stratified discharge was obtained as before.
60 Royal Socieiy : —
^vhile little or no chemical action took place in the battery ; on heating
the potassa, the character of the stratitications gradually changed, and
suddenly a remarkably brilliant ^Yhite discharge, also stratified, was
observed ; intense chemical action was at the same time perceptibly
taking place in the battery, and on breaking the circuit, the usual vivid
electrical flame-discharge was developed at the point of disruption.
The continuation of these experiments will necessarily occupy much
time, involving, as they do, the charging of so extended a series of
the nitric acid battery, and with the requisite care necessary for
the proper insulation of each cell. Other phenomena were observed
which require further verification ; but I hope that after the recess the
result which I hope to obtain may be of sulhcient interest to form the
subject of a future communication.
" Note on the Transmission of Radiant Heat through Gaseous
Bodies." By John Tyndall, Ph.D., F.R.S. &c.
Before the Roval Society terminates [its present session, I am
anxious to state the nature and some of the results of an investiga-
tion in which I am now engaged.
With the exception of the celebrated memoir of M. Pouillet on Solar
Radiation through the atmosphere, nothing, so far as I am aware,
has been published on the transmission of radiant heat through
gaseous bodies. We know nothing of the effect even of air upon
heat radiated from terrestrial sources.
The law of inverse squares has been proved by Melloni to be
true for radiant heat passing through air, whence that emmeut
experimenter inferred that the absorption of such heat by the atmo-
sphere, in a distance of 18 or 20 feet, is totally inappreciable.
With regard to the action of other gases upon heat, we are not, so
far as I am aware, possessed of a single experiment.
Wishing to add to our knowledge in this important particular, I
had a tube constructed, 4 feet long and 3 inches in diameter, and
by means of brass terminations and suitable washers, I closed per-
fectly the ends of the tube by polished plates of rock-salt. Near to
one of its extremities, a T-piece is attached to the tube, one of
whose branches can be screwed to the plate of an air-pump, so as to
permit the tube to be exhausted ; while the gas to be operated on is
admitted through the other branch of the T-piece. Such a tube
can be made the channel of calorific rays of every quaUty, as the
rock-salt transmits all such rays with the same facility.
I first permitted the obscure heat emanating from a source placed
at one end of the tube, to pass through the latter, and fall upon a
thermo-electric pile placed at its other end. The tube contained
ordinary air. When the needle of a galvanometer connected with
the pile had come to rest, the tube was exhausted, but no change in
the position of the needle was observed. A similar negative result
was obtained when hydrogen gas and a vacuum were compared.
Here I saw, however, that when a copious radiatiou was employed,
and the needle pointed to the high degrees of the galvanometer, to
cause it to move through a sensible space, a comparatively large
On the Trammission of Radiant Heat through Gaseous Bodies. Gl
diminution of the current would be necessary ; far larger, indeed, than
the absorption of the air, if any, could produce : while if I used a
feeble source, and permitted the needle to point to the lower degrees
of the galvanometer, the total quantity of heat in action was so
small, that the fraction of it absorbed, if any, might well be insensible.
My object then was to use powerful currents, and still keep the
needle in a sensitive position ; this was effected in the following
manner : — The galvanometer made use of possessed two wires coiled
side by side round the needle ; and the two extremities of each wire
were connected with a separate thermo-electric pile, in such a manner
that the currents excited by heat falling upon the faces of the two piles
passed in opposite directions round the galvanometer. A source of
heat of considerable intensity was permitted to send its rays through
the tube to the jjile at its opposite extremity ; the deflection of the
needle was very energetic. The second pile was now caused to ap-
proach the source of heat until its current exactly neutralized that of
the other pile, and the needle descended to zero.
Here then we had two powerful forces in perfect equilibrium ; and
inasmuch as the quantity of heat in action was very considerable, the
absorption of a small fraction of it might be expected to produce a
sensible effect upon tlie galvanometer-needle in its present position.
When the tube was exhausted, the balance between the equal forces
was destroyed, and the current from the pile placed at the end of the
tube predominated. Hence the removal of the air had permitted a
greater amount of heat to pass. On readmitting the air, the needle
again descended to zero, indicating that a portion of the radiant heat
was intercepted. Very large effects were thus obtained.
I have aj)plied the same mode of experiment to several gases and
vapours, and have, in all cases, obtained abundant proof of calorific
absorption. Gases vary considerably in their absorptive power — pro-
bably as much as liquids and solids. Some of them allow the heat
to pass through them with comparative fi\cility, while other gases
bear the same relation to the latter that alum does to other diather-
manous bodies.
Different gases are thus shown to intercept radiant heat in different
degrees. I have made other experiments, which prove that the self-
same gas exercises a different action iq)on different qualities of radiant
beat. The investigation of the subject referred to in this Note is
now in })rogres3, and I hope at some future day to lay a full descrip-
tion of it before the Royal Society.
"Photochemical Researches." — Part IV. By Robert "\V. Bunsen,
For. Memb. R.S., and Henry Enfield Roscoe, Ph.D., Professor of
Chemistry in Owens College, Alanchestcr.
In the three cominnnieations'^ which they have already made to the
Royal Society upon the subject of photochemistry, the authors showed
that they have constructed a most delicate and trustworthy instrument
by which to measure the chemical action of light, and by help of which
they have been able to investigate the laws regulating this action.
* riiil. Trans. ISoJ, pp. oof), 381 and GOl.
62 Royal Society : —
In the present memoir, the authors proceed, in the first place, to
estabUsh a general and absolute standard of comparison for the
chemical action of light ; a:id in the second place, to consider
the quantitative relations of the chemical action effected by direct
and diffuse sunlight. They would endeavourj in this part of their
research, to lay the foundation of a new and important branch of
meteorological science, by investigating the laws which regulate the
distribution, on the earth's surface, of the chemical activity ema-
nating from the sun.
The subject-matter of the present communication is divided under
five heads : —
1. The comparative and absolute measurement of the chemical
rays.
2. Chemical action of diffuse daylight.
3. Chemical action of direct suuUght.
4. Photochemical action of the sun, compared with that of a
terrestrial source of light.
5. Chemical action of the constituent parts of solar light.
The first essential for the measurement of photochemical actions,
is the possession of a source of constant light. This the authors
secured Avith a greater amount of accuracy than by the method de-
scribed in their former communications, by employing a flame of pure
carbonic oxide gas, burning from a platinum jet of 7 millims. in dia-
meter, and issuing at a given rate, and under a pressure very slightly
different from that of the atmosphere. The action which such a
standard flame produces in a given time on the sensitive mixture of
chlorine and hydrogen, placed at a given distance, is taken as the
arbitrary unit of photochemical illumination. This action is, how-
ever, not that which is directly observed on the scale of the instru-
ment. The true action is only obtained by taking accoimt of the
absorption and extinction which the hght undergoes in passing
through the various glass-, water-, and mica-screens placed between
the flame and the sensitive gas. These reductions can be made by help
of the determinations given in Part III. of these Researches, as well
as by experiments detailed in the present Part. When these sources
of error are eliminated, it is possible, by means of this standard
flame, to reduce the indications of different instruments to the same
unit of luminous intensity, and thus to render them comparable.
For this purpose, the authors define the photometric unit for the
chemically active rays, as the amount of action produced in one
minute, by a standard flame placed at a distance of one metre
from the normal mixture of chlorine and hydrogen ; and they
determine experimentally for each instrument the number of such
units which correspond to one division on the scale of the instru-
ment. By multiplying the observed number of divisions by the
number of photometric units equal to one division, the observations
are reduced to a comparable standard. It is proposed to call this
unit a chemical unit of light, and ten thousand of them one chemical
degree of light.
According to this standard of measiu-ement, the chemical illu-
Messrs. Bunsen and Roscoe's Photochemical Researches. 63
mination of a surface, that is, the amount of chemically active light
which falls perpendicularly on the plane surface, can be obtained.
It has thus been found that the distance to which two flames of
coal-gas and carbonic oxide, each fed with gas at the rate of 4*105
cubic cent, per second, must be removed from a plane surface, in order
to effect upon it an amount of chemical action represented by one
degree of light, was, in the case of the coal-gas flame, 0*929 metre,
iu that of carbonic oxide 0'5G1 metre. The chemical illuminating
power, or chemical intensity, of various sources of light, measured
by the chemical action effected by these sources at equal distances
and in equal times, can also be expressed in terms of this unit of
light ; and these chemical intensities may be compared with the
visible light-giAang intensities. In like manner, the authors define
chemical brightness as the amount of light, measured photochemi-
cally, which falls perpendicularly from a luminous surface upon a
physical point, divided by the apparent magnitude of the surface ;
and this chemical brightness of circles of zenith-sky of difl'erent sizes
has been determined. Experiment shows that the chemical bright-
ness of various sized portions of zenith- sk};-, not exceeding 0*00009
of the total heavens, is the same ; or, that the chemical action
effected is directly proportional to the apparent magnitude of the
illuminating surface of zenith-sky.
It is, however, important to express the photochemical actions
not only according to an arbitrary standard, but in absolute measure,
in imits of time and space. This has been done by determining
the absolute volume of hydrochloric acid formed by the action of a
given source of light during a given space of time. For this pur-
pose, we require to know —
t'=the volume of hydrochloric acid formed by the unit of light.
A = the thickness of sensitive gas through which the light passed.
<y=the surface-area of the insulated gas.
a = the coefficient of extinction of the chlorine and hydrogen for
the light employed.
Z=the number of observed units of light in the time t.
When these values are known, the volume of hydrochloric acid
which would be formed in the time t, by the rays falling perpendi-
cularly on the unit of surface, if the light had been completely
extinguished by passing through an infinitely extended atmosphere
of dry chlorine and hydrogen, is found from the expression
V=:^ . -i
q l-io""'**
In this way the chemical illumination of any surface may be ex-
pressed by the heigbt of the column of h)-drochloric acid which
the light falling upon that surface woidd ju-oduce, if it passed
through an unlimited atmosphere of chlorine and hydrogen. This
height, measured in metres, the authors propose to call a Licjht-
metre. The chemical action of the solar rays can be expressed in
light-metres ; and the moan daily, or annual height thus obtained,
dependent on latitude and longitude, regulates the chemical chmate
64 Royal Society : —
of a place, and points the way to relations for the chemical actions
of the solar rays, which in the thermic actions are already repre-
sented by isothermals, isotherals, &c.
In order to determine the chemical action exerted by the whole
diffuse daylight upon a given point on the earth's surface, the
authors were obliged to have recourse to an indirect method of ex-
perimenting, owing to the impossibility of measuring the whole
action directly, by means of the sensitive mixture of chlorine and
hydrogen. For the purpose of obtaining the wished-for result, the
chemical action proceeding from a portion of sky at the zenith, of
known magnitude, was determined in absolute measure, and then,
by means of a photometer, whose peculiar construction can only be
understood by a long description, the relation between the visible
illuminating power of the same portion of zenith sky and that of
the total heavens was determined. As, in the case of lights from
the same source but of different degrees of intensity, the chemical
actions are proportional to the visible illuminating effects, it was
only necessary, in order to obtain tlie chemical action produced by
the total diffuse light, to multiply the chemical action of the zenith
portion of sky by the number representing the relation between the
visible illumination of the total sky and that of the same zenith
portion.
The laws according to which the chemical rays are dispersed by
the atmosphere can only be ascertained from experiments made
when the sky is perfectly cloudless. In the determinations made
with this specially-arranged photometer, care was therefore taken
that the slightest trace of cloud or mist was absent, and the relation
between the visible illuminating effect of a portion of sky at the
zenith and that of the whole visible heavens, was determined for
every half-hour from sunrise to sunset ; the observations being made
at the summit of a hill near Heidelberg, from which the horizon was
perfectly free.
The amount of chemical illumination which a point on the earth's
surface receives from the whole heavens, depends on the height of
the sun above the horizon and on the transparency of the atmo-
sphere. If the atmospheric transparency undergoes much change
when the sky is cloudless, a long series of experiments must be made
before the true relations of atmospheric extinction of the chemical
rays can be arrived at. The authors believe, however, founding
their opinion on the statement of Seidel in his classical research on
the luminosity of the fixed stars, that the alterations in the air's
transparency with a cloudless sky are very slight ; and they there-
fore think themselves justified in considering the chemical illumi-
nation of the earth's surface, on cloudless days, to be represented
simply as a function of the sun's zenith distance. Although, from the
comparatively small number of experiments which have been made,
owing to the difficulty of securing perfectly cloudless weather, the
constants contained in the formula; cannot lay claim to any very
great degree of accm-acy, the authors believe that the numbers ob-
tained are sufficient to enable them to determine the relation accord-
Messrs. Bunsen and Roscoe's Phofochemical Researches. 65
ing to which the chemical energy proceeding from the sun is diffused
over the earth when the sky is unclouded.
From a series of ohservatious made on June 6, 1858, the relation
between the amount of light optically measured falling from the
whole sky, and the amount (taken as unity) which, at the same
time, falls from a portion of zenith sky equal to yJ^j-^th of the whole
visible heavens, has been calculated for every degree of sun's zenith
distance from 20° to 90° ; the results being tabulated, and also
represented graphically. These numbers, multiplied by the che-
mical light proceeding from the same portion of zenith sky for the
same zenith distances, must give the chemical action effected by the
whole diffuse daylight. The amount of chemical light wliich falls
from the zenith portion of sky is, however, the chemical brightness
of that portion of sky. This chemical brightness has been deter-
mined, by the chlorine and hydrogen photonieter, on various days,
and at different hours, when the sky was j)erfectly cloudless. A
table contains the chemical action, expressed in degrees of light,
which is effected on the earth's surface by a portion of zenith sky
equal in area to y^jLyth of the whole visible heavens, under the cor-
responding sun's zenith distances from 20° to 90°. A curve repre-
senting the relation between the action and the height of the sun,
shows that although the single observations were made on different
years and at different times of the year and day, they all agree
closely amongst themselves, and hence another proof is gained of the
slight effect which variation in the air's transparency produces ; and
it is seen that the total chemical action effected by the diffuse light
of day may be represented as a function of the sun's zenith distance.
The numbers thus obtained have only to be multiplied by the
corresponding numbers of the former table, in order to give the
chemical action effected by the total diffuse light of day for zenith
distances from 20° to 90°. A table and graphic representation of
these numbers is given. Knowing the relation between the sun's
altitude and the chemical action, the chemical illumination effected
each miniite at any given locality at a given time may be calculated ;
this calculation has been made for a number of ])laces for each hour
on the vernal equinox, tables and curves representing the alteration
of luminous intensity with the height of the sun at these places being
given.
From these data it is possible also to calculate the action produced
by the whole diffuse light, not only for each minute, Ijut during any
given space of time. For the following jjlaces the amount of che-
mical illumination expressed in degrees of light which falls from sun-
rise to sunset on the vernal equinox, is —
Melville Island 10590
Reykiavik 15020
St. Petersburg i til 1 0
Manchester 18220
Heidelberg 19100
Naples 20550
Cairo 2i(i70
Phil. Mag. S. !•. Vol. 19. No. 13 !•. Jan. 18()t). F
66 Royal Society : —
Experiment lias shown tliat clouds exert the most powerful influ»
ence in reflecting the chemical rays ; when the sky is partially
covered by light white clouds, the chemical illumination is more than
four times as intense as when the sky is clear. Dark clouds and
mists, on the other hand, absorb almost all the chemically active
rays.
The chemical action of the direct sunlight was determined by
allowing a known fractional portion of the solar rays to fall perpen-
dicvilarly on the insolation vessel of the chemical photometer. The
solar rays reflected from the mirror of a Silbermann's heliostat
were passed through a fine opening of known area into the dark
room, and a large number of reductions and corrections had to be
made in order to obtain, from the direct observations, the action,
expressed in degrees of light, which the sun shining directly upon
the apparatus would have produced if no disturbing influences had
interfered. This action of direct sunshine was determined on three
different cloudless days for various altitudes of the sun. As the sun
approached the zenith the observed action rapidly increased ; thus
at 7^ 9' A.M., on September 15, 1858, when the sun's zenith
distance was 76° 30', the reduced action amounted to 5"5 degrees of
light, whilst at 9*" 14' a.m. on the same day, the zenith distance
being 58° 11', the action reached G7"6. This increase in the sun's
illuminating power is owing to the diminution in length of the
column of air through which the rays pass. If we suppose the
atmosphere to be throughout of the density corresponding to a
pressure 0*70 and a temperature 0°, and consider it as a horizontal
layer, and if A represent the action effected before entrance into the
atmosphere, the action, when the ray has passed through a thickness
of atmosphere = I, is represented by
W,=A10""',
where- signifies the depth of atmosphere through which the ray
has to pass to be reduced to -J^th of its original intensity, and where
I is dependent on the atmosphere's perpendicular height =A, and
the sun's zenith distance (p. The numerical values of A a and / may
be calculated from the direct observations, and hence the action Wj
effected at any other zenith distance 0^, and under a pressure Pj, is
found from the equation
-rih Pi
W^=A10 ^°««'>Po,
where P^ represents the atmospheric pressure under which A and a
are calculated. A comparison between the actions W, thus obtained,
and those, W^^, found by experiment, shows as close an agreement as
could be expected where the observational errors are necessarilv so
large.
From these experiments it is seen, that if the sun's ravs were not
weakened by passage thi-ough the atmosphere, they would produce
an illumination represented by 31 S degrees of light; or they would
effect a combination in one minute on a surface on which they fell
Messrs. Bimsen and Roscoe^s Photochemical Researches. 67
perpendicularly, of a column of hydrochloric acid 35*3 metres in
height, assuming tliat the rays are extinguished by passing through
an infinitely extended atmosphere of chlorine and hydrogen. By
help of the above formula, it is also found that the sun's rays, after
they have passed in a perpendicular direction through the atmo-
sphere to the sea's level, under a mean pressure of 0*76 metre, only
effect an action of 14*4 light-metres, or that under these conditions
nearly two-thirds of their chemical activity have been lost by extinc-
tion and dispersion in the atmosphere. The total chemical action
emanating from the sun during each minute is therefore represented
by a column of hydrochloric acid 3.5 metres in height, and having
an area equal to the surface of a sphere whose diameter is the mean
distance of the earth to the sun. Or the light which the sun
radiates into space during each minute of time represents a chemical
energy, by means of which more than 25 billions of cubic miles of
chlorine and hydrogen may be combined to form hydrochloric acid.
In like manner the amounts of chemical action have been calculated,
which the sun's rays, undiminished by atmospheric extinction, pro-
duce at the surface of the chief planets. The first column of num-
bers gives the mean distances of the planets from the sun, the second
contains the chemical action expressed in light-metres.
Mercury 0-387 235-4 light-metres.
Venus 0-723 67-b „
Earth 1-000 35-3 „
Mars 1-524 15-2 „
Jupiter 5-203 1-3 „
Saturn 9-539 0*4 „
Uranus 19-183 0-1
Neptune 30-040 0-04
By aid of the formula already given, the authors have been enabled
to calculate the chemical action effected each minute by the direct
sunlight, not only at different points on the earth's surface, but at
various heights above the sea's level. Both these series of relations
are tabulated, and graphically represented. On comparing the
numbers and curves giving the action of the total diffuse light with
those of the direct solar light, the singular fact becomes apparent,
that from the North Pole to latitudes below that of Petersburg,
the chemical action proceeding from the diffuse light is, throughout
the day on the vernal equinox, greater than that effected by the
direct sunlight ; and that in lower latitudes, down to the Equator,
the same phenomenon is observed, if not for the whole, still for a
portion of the day. It is further seen, that for all places, and on
every day when the sun rises to a certain height above the horizon,
there is a moment at which the chemical action of the diffused light
is exactly equal to that of tlie direct sunlight. The times at which
these i)hases of equal chemical illumination occur can be calculated ;
they can also be actually determined, by allowing the direct sunlight
alone, and the whole diffuse daylight alone, to fall at the same time
upon two pieces of the same sensitized photographic paper; the
period at which both papers become equally blackened, gives the
F2
68 Royal Society : —
time of the ])liase of equal cliemical intensity. Experiment proved
not only that these points of equality which the theory rcquh-es
actually occur, hut also that the agreement hetween the calculated
and observed times of occurrence of the phases is very close, giving
proof that the data upon which the theory is founded are substan-
tially correct.
The formula, by help of which the chemical action of the direct
sunlight effected at any place during any given time can be calcu-
lated, is next developed, and the direct solar action at the following
places calculated for the vernal equinox from sunrise to sunset.
Column I. gives the action of the direct sunlight during the whole
day, expressed in degrees of light; Column II. the action for the
same time effected by both direct and diffuse solar light ; and
Colmnn III. the same action expressed in light-metres : —
I. II. III.
Melville Island 11 96 11 790 1306 metres.
Reykiavik 5964 20980 2324 „
St. Petersburg 892/ 25340 2806
Manchester 14520 32740 3625 „
Heidelberg. 18240 3/340 4136 „
Naples 26640 47190 5226 „
Cairo 36440 58110 6437 „
The authors next proceed to examine the chemical brightness of
the sun compared with a terrestrial source of light. For this pur-
pose the intensely bright light ])roduced by a wire of magnesium
burning in the air was employed. Experiment showed that the
chemical intensity of the sunlight, xindiminished by atmospheric
extinction, is 128 times greater than that from a surface of incan-
descent magnesium of like apparent magnitude ; or that burning
magnesium effects the same chemical illumination as the sun when
9° 53' above the horizon, supposing of course that both luminous
sources present to the illuminated surface the same apparent magni-
tude. A totally different relation was found to exist between the
visible illuminating power, {. e. the effect produced on the eye, of
the two sources in question. Thus, when the sun's zenith distance
was 67° 22', the chemical brightness of that source was 36"6 times,
but the visible brightness 525 times as large as that of the terrestrial
source of light.
In the last section of this communication the chemical action of
the constituent parts of the solar spectrum is investigated. The
sun's rays were reflected from a Silbermann's heliostat, and after
passing through a narrow slit, they were decomposed by two quartz
prisms. The spectrum thus produced was allowed to fall upon a
white screen covered with a solution of quinine, and any desired por-
tion of the rays could be measured by a finely-divided scale, and the
position noted by observation of the distances from the fixed lines.
For the purpose of identifying the fixed lines in the lavender rays,
the authors were, by the kindness of Mr. Stokes, allowed the use of
an unpublished map of the most refrangible portion of the spectnnn,
l)reparcd by that gentleman. As the various components of white
Dr. Simpson on the Action of Acids on Ghjcol. 69
light are unequally absorbed by the atmosphere, it was obviously
necessary to conduct all the measurements so quickly after one
another, that no appreciable difiference in the thickness of the column
of air passed through should occur.
This has been accomplished, and a series of exact measurements
of the chemical actions of the spectrum for one particular zenith-
distance of the sun obtained. The action on the sensitive gas shows
the existence of several maxima of chemical intensity in the spectrum.
Between the lines G in the indigo and II in the violet the greatest
action was observed, whilst another maximum was found to lie near
the line I in the vdtra-violct rays. Towards the red or least refran-
gible end of the spectrum, the action became imperceptible about the
line D in the orange, but at the other end of the spectrum the action
was found to extend as far as Stokes's line U, or to a distance from
the line II greater than the total length of the ordinary visible spec-
trum. Tables and curves representing the action are given.
"On the Action of Acids on Glycol." (Second Notice). By
Dr. Maxwell Simpson.
Since my last communication (Phil. ^lag. Dec. 1859) *, I have dis-
covered a more convenient process for the preparation of chloracetine
of glycol. I have ascertained that the monoacetateof glycol is as readily
converted into this substance by the action of hydrochloric acid, as a
mixture of acetic acid and glycol. As the monoacetate is easily ob-
tained, and for this i)urpose need not be quite pure, it is possible bv
this method to prepare the body in question on a large scale and
with great facility. It is simply necessary to conduct a stream' of
dry hydrochloric acid gas into the monoacetate, maintained at the
temperature of 100°C., till the quantity of oil precipitated on the
addition of water ceases to increase. The whole is then v.ell washed
with water, dried by means of chloride of calcium, and distilled.
Almost the entire quantity passes over between 144° and 146° C.
A portion of liquid prepared in this manner gave the foUowuio-
numbers on analysis, which leave no doubt as to its identity : —
Theorv. Experiment.
C, 39-18 39-01
II .T-71 0-83
O,'.... 26-14
CI 28-97
100- 00
The reaction which gives birth to this body may be thus ex-
plained : —
C.H. ] C.II.
C. H3 O, I O, + HC1= C, U3 O, \ 0, + 2H0.
CI
I have made a determination of the vapour-density of chloracetine,
and obtained results contirmatory of the formula I have given for
this body: experimental va|)0ur-densitv 4-3GI), calculated 4-231 for
4 volumes. 1 have also ascertained that oxide of ethylene is formed,
70 Royal Society : —
and not glycol, when this substance is acted upon by a solution of
potash. The following equation will explain the reaction : —
c;h;oJ^^+-h}^^=^'k ^'l^^+^^^+^^^^^^+'^^-
'ci
Action of Chloracetine of Glycol on Butyrate of Silver. — Formation
of Butyroacetate of Glycol.
Equivalent quantities of chloracetine and butyrate of silver were
exposed in a balloon with a long neck to a temperature ranging be-
tween lOU^-and 200^ C; till all the silver salt had been converted into
chloride. The product was then digested with ether, filtered, and
the filtered liquor submitted to distillation. As soon as all the ether
had been driven off, the thermometer rose rapidly to 180% and be-
tween that temperature and 215° almost the entire quantity passed
over. This was fractioued, and the portion distilling between 208°
and 215° was set apart for analysis. The numbers obtained lead to
the formula C^ Hg 0, V O^ as will be seen from the following per-
CaH,o:j
centage Table : —
Theory. Experiment.
I.
II.
c.s;. .
..55-17
54-31
55-58
Hu-.
.. 8-04
8-20
7-97
O3..
..36-79
••
100-00
I also made a determination of the acids by heating a weighed
quantity of the ether with hydrate of baryta in the usual manner.
The quantity of sulphate of baryta obtained indicated 2-2 equivalents
of acid for one equivalent of the substance analysed. The excess of
acid was probably owing to the presence in the ether of a trace of
free butyric acid. The following equation will explain the reaction
which causes the formation of this compound : —
J ^^S J c H.O.J
CI
In many reactions chlorine replaces, and is replaced by, H + O^ ; in
this it is replaced by the group C, H. O^ (equivalent to one atom of
hydrogen) +0,.
This ether, which I may call butyroacetate of glycol, has a bitter
pungent taste. It is insoluble in water, but soluble in alcohol. It is
specifically heavier than water. It is a very stable body, — solution of
potash, even when boiling, effecting its decomposition Avith difficulty.
I have no doubt that many analogous compounds may be prepared
in the manner I have just described.
Action of Chloracetine of Glycol on Ethylate of Ssda.
In the hope of forming a compound intermediate between diace-
Dr. Simpson on the Action of Acids on Glycol. 71
tate of glycol and diethylglycol, I resolved to try the actiou of chlor-
acetiue on ethylate of soda, thinking that probably the body in
question might be generated by the following reaction : —
C, H3 O, I 0,+^^^^ j 0,=C, H3 O, I 0. + NaCI.
CI
In order to settle this point, I exposed equivalent quantities of
these bodies in a sealed balloon to the temperature of a water-bath
for about two hours. My expectations, however, were not realized.
On opening the balloon, I found that the reaction had proceeded too
far, acetic ether having been formed along with the chloride of
sodium.
Action 0/ Hydrochloric and Butyric Acids on Glycol. — Formation of
Chlorhiityrine of Glycol.
This compound is prepared in the same manner as its homologue,
namely by transmitting a stream of dry hydrochloric acid gas
through a mixture of equivalent quantities of butyric acid and glycol,
maintained at the temperature of 100° C. As soon as the reaction
is finished, the product is well washed with water, dried by means
of chloride of calcium, and distilled. The greater part passes over
between 1 G0° and 1 82°. This must be rectified, and the quantity dis-
tilling between 175° and 182° collected apart. This gave, on analysis,
results agreeing with the formula p^ tt* n I ^2' ^ ^^ be seen from
the following table : — CI
I.
II.
c,,..
. . 47-84
47-76
, ,
Hu
.. 7-30
7-31
0, ..
..21-28
^ ^
Cl ..
. . 23-58
23-8
The reaction, to which the formation of this body is due, may be
thus explained : —
^^g^|0,-f^^^^g^}0,-fHCl = ^;^^Q }0, + 4H0.
'ci
Chlorbutyrine of glycol, as I may call this compound, has a jnni-
gent and somewhat bitter taste. It boils at about 180°. Its specific
gravity at zero is r0854. It is insoluble in water, but freely soluble
in alcohol. It is decomposed with difficulty by a boiling solution of
potash, but readily by solid jiotash, — chloride of potassium, butyrate
of potash, and oxide of ethylene, being formed.
I have ascertained that acctobutyrate of glycol, the ether I have
already described, can be prepared from this body as well as from
chloracetine, by exposing it to the actiou of acetate of silver. The
process is the same as that I have already given, with this difference,
that the reactuis; bodies must not be heated above 150° C. The
72 Royal Society ; —
ether prepared in tliis manner gave the following numbers on ana-
lysis : —
Theory. Experiment.
C, 55-17 56-29
H,',.... 8-04 8-75
O, .. ..36-79
The quantity of this substance at my disposal was so small (the
greater part of my product having been lost) that I could not purify
it completely ; hence the exj)erimcntal numbers do not exactly accord
with the theoretical.
Action of Hydrochloric and Benzoic Acids on Glycol. — Formation
of Chlorbenzoate of Glycol.
A mixture of equivalent quantities of glycol and benzoic acid, pre-
viously fused and powdered, was exposed to the action of dry hydro-
chloric .acid gas for several hours, the mixture being maintained at
the temperature of 100° during the action of the acid, as in the case
of the former compounds. The product thus formed presented the
appearance of a soft white solid, and contained a considerable quan-
tity of uncombined benzoic acid. This was removed by agitating it
with hot water, till, on cooling, it no longer became solid, but re-
mained ])erfectly fluid. Finally it was dissolved in alcohol, and pre-
cipitated by water. The body thus prepared, and without being
distilled, was analysed, having been previously dried in vacuo over
sulphuric acid. Another specimen, prepared in the same manner,
at a different time, was also analysed, having, however, been previ-
ously distilled. During the distillation it was observed that not a
drop of fluid passed over till the mercury had risen to 254°, and be-
tween that temperature and 270° the entire liquid distilled over.
What passed over between 260° and 270° was collected separately;
this was the portion analysed. The numbers obtained on analysis
agree with the formula ^^^ ri r\ \ O^.as the following Table shows: —
'ci
Theory.
Exiierinienl.
Portion distilled.
C,,. . . . 58-. 54
H,.... 4-87
0^.... 17-35
Cl .... 19-24
I. II.
59-70
5-01
17-93
58-69
5-31
100-00
The portion not distilled contained doubtless a trace of free ben-
zoic acid, which would affect the carbon and chlorine, but not the
hydrogen.
Chlorbenzoate of glycol, as I shall call this compound, has a
Dr. Simpson on the Action of Acids on Glycol. 73
pungent and somewhat bitter taste. It is insolable in water, but
freely soluble in alcohol and ether. Boiling solution of jjotash
effects its decomposition with ditficuUv, solid potash readily, the re-
action being the same as in the case of the analogous compounds.
Action of Hydr iodic Acid on Glycol. — Formation of Iodide of
Ethylene and lodhydrine of Glycol.
Ilydriodic acid gas is absorbed with great energy by glycol. A
considerable quantity of heat is evolved during the passage of the
gas, and the liquor becomes black and thick from the separation of
free iodine. On removing the iodine by means of dilute potash, a
mass of small white crystals is brought to light, which I at once
suspected to be iodide of ethylene. To remove all doubt on this
point, I submitted the crystals to analysis, having previously purified
them by recrystallizing from boiling alcohol. The numbers ob-
tained agree with the formula of iodide of ethylene : — ■
Theory.
Experiment.
c.
.... S-51
8-73
H,
... 1-42
1-78
In
.... 90-07
, ,
100-00
The reaction which causes the formation of iodide of ethylene may
be thus explained : —
'^^' j 0. + 2HI=C,HJ, + 4HO.
That the action of hydriodic acid on glycol should be different
from that of hydrochloric arid is doubtless owing to the bond of
union between hydrogen and iodine being much weaker than that
between hydrogen and chlorine.
If, on the other hand, the temperature of the glycol be prevented
from rising during the passage of the hydriodic acid gas, by sur-
rounding the vessel containing it with cold water, a liquid ])roduct is
obtained, which is coloured dark-brown by free iodine. This I have
not as yet been able to discover any means of purifying, it being
soluble in water, and decomposed by distillation. I believe, how-
ever, it is the compound corresponding to chlorhydrine of glycol
( ' n' f ^2/ discovered by M. Wurtz. A portion of this liquid,
CI
from which I had simply removed the free iodine, by agitation with
mercury, gave, on analysis, numbers agreeing tolerably well with the
formula of iodhydrine of glycol. After the analysis, however, I dis-
covered that it contained a considerable quantity of iodide of mercury
in solution. Another ])ortion, from which I had removed the iodine
by means of metallic silver, gave, on analysis, 11-1 per cent, carbon
74 Royal Society.
and 3-5 hydrogen, instead of 13-9 carbon and 3-0 hydrogen. After
all, an analysis is not necessary to enable us to arrive at the composi-
tion of this body. The products formed by the action of potash on
it furnish us with almost as convincing a proof of its composition as
any analysis could do. They are iodide of potassium and oxide of
ethylene.
lodhydrine of glycol is soluble in water and alcohol, but insoluble
in ether. It has no taste at first ; after a time, however, it almost
burns the tongue, it is so pungent. It is decomposed b}' heat into
iodide of ethylene, and probably glycol. It acts with great energy
on the salts of silver.
Action of Hydr iodic and Acetic Acids on Glycol. — Formation of
lodacetine of Glycol.
A stream of hydriodic acid gas was conducted into a mixture of
equivalent quantities of glacial acetic acid and glycol, the tempera-
ture of which was prevented from rising during the action of the gas.
As soon as a portion of the liqiud gave a considerable quantity of an
oily precipitate on the addition of water, the passage of the gas
was interrupted ; for the prolonged action of the gas is apt to give
rise to the formation of iodide of ethylene. The liquid thus obtained
was well washed with very dilute potash, dried in vacuo, and ana-
ri TT •)
lysed. The numbers obtained lead to the formula p^ tt^ /~j [ 0,„ as
will be seen from the following Table : — I
Theory.
Experiment.
C,.... 22-42
H,.... 3-27
0,.... 14-96
I 59-35
I. II.
21-95 22-30
3-31 3-50
100-00
lodacetine has a sweetish pungent taste. It is insoluble in water,
but soluble in alcohol and ether. Its specific gravity is greater than
that of water. It crystallizes in tables when exposed to cold. Heated
with potash, it gives iodide of potassium, acetate of potash, and oxide
of ethylene. It is readily decomposed by the salts of silver.
This compound can also be prepared with great facility by ex-
posing monoacetate of glycol to the action of bydriodic aoid gas.
The liquid must be kept cold during the action of the gas, which
should be interrupted as soon as the addition of water to a portion
of it causes an abundant oily precipitate. The whole is then washed
with dilute potash, and dried in vacuo. A specimen prepared in
this manner gave, on analysis, 22'G2 per cent, carbon and 3*43 hy-
drogen, instead of 22-42 carbon and 3*27 hydrogen.
I hope soon to have an opj)ortunity of studying these iodine com-
pounds more particularly.
Geological Society. 79
Action of Anhydrous Acetic Acid on Glycol. — Formation of Mono-
acetate of Glycol.
A mixture of equivalent quantities of anhydrous acetic acid and
glycol was heated in a sealed tube for several hours at a temperature
not exceeding 1 70° C. On opening the tube, and submitting its
contents to distillation, it was observed that the mercury remained
stationary for a considerable time at about 120°, the point of ebulli-
tion of glacial acetic acid, and then rose rapidly to 180°, between
which and 186° the remainder of the liquid passed over.
This was analysed, and proved to be pure monoacetate of glycol.
Theory.
Experiment.
C,.. ..46-15
46-02
H,.... 7-69
7-80
0,.... 46-16
••
100-00
The following equation will explain the reaction which takes place
between the acid and the glycol : —
C,H,
H3
H
The foregoing experiments were performed in the laboratory of
M. Wurtz.
GEOLOGICAL SOCIETY.
[Continued from vol. xviii. p. 479.]
November 30, 1859. — Prof. John Phillips, President, in the Chair.
The following communications were read : —
1. " On some Bronze Relics from an Auriferous Sand in Siberia."
By T. W. Atkinson, Esq., F.G.S.
During the author's stay at the gold-mine on the River Shargan,
in Siberia (Lat. 59° 30' N. and Long. 96° 10' E.) in August 1851,
some fragments of worked bronze were dug up by the workmen, at
u depth of 14 feet 8 inches below the surface, from a bed of sand in
wliich gold-nuggets occur. This sand rests on the rock, and is
covered by beds of gravel and sand, overlain by '2 feet of vegetable
soil. The fragments appear to have belonged either to a bracelet
or to some horse-trappings.
2. " On the Volcanic Country of Auckland, New Zealand." By
Charles Hcaphy, Esq. Communicated by the President.
The isthmus-liUe district of Auckland and its neighbourhood,
described by Mr. Heaphy as a basin of Tertiary deposits, is bordered
76 Geological Society : —
by clay-slate, igneous rocks, and at one spot on the south by creta-
ceous strata ; and it is dotted by upwards of sixty extinct volcanos,
often closely situated, and showing in nearly every instance a well-
defined point of eruption, generally a cup-like crater, on a hill about
300 feet high. Interesting instances of successive volcanic eruption
are numerous all over this district, 60 miles round Auckland ; and
there seems to have been four distinct epochs of eruption, thus
classified by Mr. Heaphy : — 1. The first was that which raised the
trachytic mountains and the black boulder-like igneous rock.
2. Then came the eruptions in the Tertiary period, the ashes
of which form beds in the Tertiary rock. 3. Then the eruptions on
the upheaval of the Tertiary cliffs : these appear as cones above
faults on the Tertiary beds and on the edges of cliffs. 4. Lastly
the eruptions that have broken through the Tertiary beds, and the
lava-streams of which follow the natural valleys of the country.
The volcanic phaenomena were illustrated by maps and numerous
sketches by the author. Some Tertiary Terebratulce, some few
fossil plants, and some Cretaceous fossils (Inoceramus and Belern-
nitella) accompanied this memoir.
3. " On the Geology of a part of South Australia." By T. Burr,
Esq. From the Colonial Office. 1848.
The lowlands about Adelaide on the west, and along the River
Murray on the east, consist of horizontal beds of limestone and cal-
careo-siliceous deposits, yellowish and reddish in colour, full of
marine fossils, and of the Tertiary age. Sometimes gypsum and
ferruginous sand replace the limestone. These plains are arid,
except where granite ])rotrudes from the surface, presenting cavities
in w'hich rain-water collects. The author observed a similar Tertiary
formation on Yorke's Peninsula, at Port Lincoln, and to the S.E. to
beyond Rivoli Bay ; and it probably forms vast tracts in New South
Wales and Western Australia. None of these tertiary districts
appear to exceed an elevation of 300 feet above the sea.
In describing two volcanos in South Australia, Mount Gambler
and IVIount Schauck, Mr. Burr remarked that, coming from the west
or north-west, at about 20 miles from these hills a white coral-lime-
stone (Bryozoan limestone) containing flint or chert, takes the place
of the limestones and calcareous sandstones, with recent sand-forma-
tion, previously passed over. This white limestone is remarkable
for the numerous deep well-like water-holes in it, within about 12
miles of the volcanic mountains and about east or west of them.
IVIount Gambler has a height of 900 feet above the sea (600 feet
above the plain), and has three craters, lying nearly east and west,
and occupied with lakes of fresh water. Mount Schauck, at a distance
of about 9 miles, magnetic south, is circular, and has one large, and
two small lateral craters.
The author next described the granite, gneiss, and slaty rocks
along a section extending from the River Murray and Kangaroo
Range, across Mount Barker and Mount Lofty, towards Adelaide ;
and noticed the mode of occurrence of the ores of copper, iron, lead,
&c. in these rocks. Lastly he noticed and expLiined the occurrence
On some Tertiary Deposits in South Australia. 77
of calcified stems of trees, standing in the position of their growth,
in the sand-dunes of the Gulf of St. Vincent, near Adelaide.
4, " On some Tertiary deposits in South Australia." By the Rev.
Julian Edmund Woods. Communicated by the President.
'J'he author, in the first place, described the geographical features
of that part of the colony of South Australia to which his observa-
tions refer. It lies between tlie R.iver Murray on the west, and the
colony of Victoria on the east; and includes an area 156 miles long,
N. and S., and 70 broad from E. to W. Some trap-dykes and four
volcanic hills are almost the only interruptions to the horizontality
of these plains, which rise graduallj' from the sea, and are occupied
by the Tertiary beds to be noticed ; they extend into Victoria for
some seventy miles, as far as Port Fairy.
In some places on the plains a white compact unfossiliferous lime-
stone lies under the surface-soil; and is sometimes 30 feet thick.
Under this is a fossiliferous limestone. The passage between the
two is gradual. This latter rock is made up of Bryozoa — perfect and
in fragments — with some Fectens, Terebratulcc, Ech'moderms, &c.
Sometimes this rock appears like friable chalk, without distinct
fossils. A large natural jjit, originating from the infalling of a cave,
occurs near the extinct volcano Mount Gambler, and is 90 feet
deep — showing a considerable thickness of this Bryozoan deposit in
several beds of 14 ft., 10 ft., 12 ft. thickness. Similar ])its show
the deposit in the same way at the Mosquito Plains, 70 miles north.
Regular layers of flints, usually black, rarely white, occur in these
beds, from 14 to 20 feet apart. These, with its colour, and with
the superficial sand-pipes, perforating the rock to a great depth, give
it a great resemblance to chalk.
The whole district is honeycombed with caves — always, however,
in the higher grounds in the undulations of the plains.
One of the caves, in a ridge on the northern side of the Mosquito
Plains, is 200 feet long, is divided into three great halls, and has
extensive side-chambers. The caves have a north and south direc-
tion, like that of the ridge. The large cave has a great stalactite
in it ; and many bones of Marsupialia are heaped up against this
on the side facing the entrance ; possibly they may have been
washed up against this barrier by an inflowing stream. The dried
cor])se of a native lies in this cave. It has been partially entangled
in the stalactite ; but this man was known to have crept into the
cave when he had been wounded, some fourteen years ago. Many
of the caves have great pits for their external apertures, and contain
much water.
Some shallow caves contain bones of existing Marsupialia, which
have evidently been the relics of animals that fell into the grass-
hidden aperture at top.
The caves appear in many cases to be connected with a subterra-
nean system of drainage ; currents and i)orio(lical oscillations being
occasionally observed in the waters contained in them. There is but
little superficial drainage. One overflowing swamp was found by
78 Intelligence and Miscellaneous Articles.
the author to send its water into an underground channel in a ridge
of limestone.
Patches of shelly sand occur here and there over the 10,980 square
miles of country occupied by the white limestones ; but near the
coast this shelly sand thickens to 200 feet.
A coarse limestone forms a ridge along the coast-line, and it con-
tains existing species of shells. This indicates an elevation of the
coast of late date, and which probably is still taking place.
XI. Intelligence and Miscellaneous Articles.
ON A NEW MINERAL CONTAINING NIOBIUM.
BY DR. JULIUS POTYKA.
rPHE author was induced by H. Rose, to undertake the investiga-
•*■ tion of a mineral received by Dr. Krantz, of Bonn, from Norway
under the name of tyrite, and sent by him to Rose. The analyses
of this mineral showed that it is probaljly a new species. Its com-
position is different both from that of Fergusonite (Weber), and from
that of tyrite (Forbes). From these two minerals it is distinguished
especially by its great amount of potash, and from tyrite also by its
containing zirconia, whilst alumina has been found in tyrite. As,
however, the locality where it occurs is stiU unknown, and its cry-
stalline form has not yet been observed, the author has not given it
a name.
The mineral received by the author forms small specimens of irre-
gular outline about 4 lines in diameter, included in red felspar. It
is not cleavable, has an uneven fracture, a black colour, and an im-
perfect metallic lustre ; the fragments exhibit a reddish brown
translucence at their edges. Its streak is reddish brown. Its hard-
ness is equal to that of apatite.
When heated before the blowpipe with borax, it furnishes a glo-
bule which is reddish yellow while hot, yellowish when cold ; in
phosphorus salt it dissolves readily, forming a clear globule, which is
greenish yellow while hot, greenish on cooling. When fused with
carbonate of soda and nitrate of potash, it gives no reaction of man-
ganese. The specific gravity of the coarse powder is 5*124 at
63°'68 F. If hot water be poured over the mineral, it crackles;
and on boiling it afterwards, air-bubbles escape — at the same time
the colour becomes pale liver-brown, but on drying it again becomes
black.
When heated in a retort, the mineral decrepitates and furnishes
milky aqueous drops with an odour of sulphuretted hydrogen, toge-
ther with traces of sublimed sulphur ; it probably contains inter-
mixed iron pyrites.
The calcined mineral is brownish yellow ; when strongly ignited
in the platinum crucible, it lost in all 3" 71 percent. Its specific
gravity was then o'319 at 64°'58 F. The mineral in very fine pow-
der is of a dingy yellow colour.
Intelligence and Miscellaneous Articles. 79
In Analysis I. the calcined mineral was decomposed by bisulphate
of potash, and in Analysis II. by sulphuric acid.
A. shows the average calculated for uncalcined mineral.
B. the amount of oxygen : —
I.
Hyponiobic acid. , . . 45' 10
Zirconia 0'83
Tungstic acid 1'40
Oxide of tin O'lO
Oxide of lead 0-43
Oxide of copper .... 0'36
Yttria 33'13
Protoxide of cerium . 3 "82
Protoxide of iron ... 1*17
Protoxide of uranium 4*28
Lime 203
Magnesia trace
Potash
Water
The amount of oxygen in the acids to that in the bases is as
1 : r04, from which we may deduce the formula 3 RO + Nb^ O^, in
which the term RO includes the bases KO, YO, CeO, UO, and
CaO. — PoggendorfF's Annalen, cvii. p. 590.
II.
A.
B.
45-24
43-49
8-58
0-80
0-21
1-35
0-28
009
002
0-41
0-03
0-35
0-07
31-90
6-35
3-68
0-53
1-12
0-24
4-12
0-49
1-95
trace
0-55
7-51
7-23
1-22
. .
3-71
3-29
THE PSEUDO-DIASCOPE. BY F, O. WARD.
By means of this instrument an aperture transmitting light is
made to produce on one eye an isolated impression, while the other
eye is directed to an opake body, such as the hand held before it.
The image of the aperture is then found to be transposed, and its
perception ceases to be assigned to the eye by which it is really seen,
— the effect being that a perforation appears in the opake body,
through which the light seems to shine upon the eye by which this
is viewed. The principle illustrated by this instrument, according
to the author's view, is the essentially goniometrical and deductive
nature of the visual act, whenever the distances of bodies are per-
ceived, and their relative positions in space assigned Proc. Lit.
and Phil. Soc. Manchester, Nov. 29, 1859.
ON THE OCCURUENCE OF UREA IN THE ORGANS OF THE PLAGI-
OSTOMOUS FISHES. BY G. STADELER.
In an investigation made last year by Frerichs and Stiidelcr, these
observers found that the Plagiostomi are distinguished from all other
fishes by their containing large quantities of urea in all their organs.
The organs and the lilood of Sci/llium cafiicula, the kidneys and
muscles of Spinax acanthias, and different organs of the Rays, con-
80 IntelUyence and Miscellaneous Articles,
tained urea in abundance, wliilst in bony fishes, as also in the Stur-
geon and Lamprey, which make the nearest approach to the Plagio-
stomi, no urea could be detected. From this it appeared that the
metamorphosis of materials in the Plagiostomi is quite different from
that in all other fishes, and the subject was of sufficient importance
to call for further investigation.
Last winter the author saw upon a table a large specimen of Raia
clavata, which had been taken at Marseilles, and sent to Zurich
during very cold weather. The author was able to procure the salt
water in which the fish was boiled, and succeeded in preparing pure
urea therefrom.
The gills, heart, liver, spleen, kidneys, pancreas, testes, the hu-
mours of the eye, the lenses and the muscles of a large specimen of
Raia Balis, which the author subsequently obtained from Havre,
contained very large quantities of urea, accompanied by the sub-
stances formerly mentioned. Xo trace of uric acid could be detected.
Creatine was found not only in the muscles, but also in the heart
and the branchiae ; in the muscles it was accompanied by another,
difficultly soluble body, which was precipitated in white flakes by
pernitrate of mercury, and also formed a compound with silver when
ammonia was carefully added. This body was therefore possibly
allantoine. The quantity of scyllite which the author obtained,
principally from the liver, was not sufficient for an elementary
analysis.
The author obtained two Torpedos from Professor Lessona of
Genoa, T. ocellata and marmorata. They were young specimens
of about 3 inches in breadth and from 4 to 5 inches long, preserved in
spirit. The alcohol had penetrated all the organs; and therefore, as
a separate examination of these could lead to no result, the objects
were pounded with powdered glass and extracted with alcohol.
The alcoholic extract was treated as already described. Urea was
present in abundance. Thus the occurrence of urea is proved with
regard to six fishes of the order Plagiostomi (viz. ScylHum canicula,
Spiuax acanthias, Raia Batis, R. clavata, Torpedo marmorata, and
T. ocellata). As regards the formation of urea in these animals, the
author indicates that, as no trace of uric acid occurs in the Rays, it
appears to be most probable that the urea is formed by the further
decomposition of creatine, the latter taking up water and splitting
into urea and sarcosine : —
Qs H9 j^-3 0V2H0 = C= H^ N= 0- + C' H" NO^
Creatine. Urea. Sarcosine.
If the above-mentioned body, precipitable by mercury and silver,
be actually allantoine, the urea might certainly be derived from this,
by its taking up water and oxygen and becoming decomposed into
carbonic acid and urea. — Journ.fiir Prakt. Chemie, Ixxvi. p. jS.
TUE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCP:.
[FOURTH SERIES.]
FEBRUARY I8C0.
XII. On Voivel Sounds. By M. Helmholtz*.
A MUSICAL note is produced by a periodical motion of the
air repeated in the same manner at equal and sufficiently
small intervals of time. The motion during each period of
oscillation may be quite arbitrary^ provided that the same motion
which took place during the first period be repeated in like man-
ner in all subsequent ones.
If, in each period of oscillation, the small particles of air move
to and fro exactly in the same manner as the centre of gravity
of a pendulum when its amplitude is very small, w^e hear only a
simple and single note, whose pitch is determined by the number
of equal periods contained in a second. In this case the velocity
as well as the pressure of the air at any point of the mass of air
in motion, may be represented mathematically by a simple ex-
pression of the form A sin {2'7Tnt + c). In a former memoir on
resultant notes {Cumbinations-Tone) , I have pointed out a method
by means of which simple pendulum-like oscillations of molecules
of air (or, as I proposed to call them, simple aerial ivaves) may be
produced. To do so I made use of tuning-forks, which, when
struck, do not communicate perceptible oscillations to the mass
of air in which they are held. But when they are held at the
mouth of a resonant tube whose deepest note is in unison with
that of the tuning-fork, this deepest note of the fork is commu-
nicated forcibly to the air. Even when the tuning-fork can give
still higher notes, it may be easily so arranged that these, its
higher notes, shall not be in unison with the higher notes of
* Translation, from Poggcndorff 's Annalen, vol. cviii. p. 280, of a paper
originally communicated bj- the Author to the Royal Bavarian Academy of
Sciences.
PhiL Mac;, S. 4. Vol. 19. No. 1.35. Feb. 18G0. , G
82 Prof. Helmholtz on Vowel Sounds.
the resonant tube, and thus, not being reinforced by the latter,
shall remain inaudible.
But when the motion of the air during a period of oscilla-
tion does not follow the simple law of the pendulum, but any
other whatever, we may in general by due attention discover
various notes, even when the motion of the air is produced by a
single sounding body. Now, according to the well-known theorem
of Fourier, every periodical motion of the air may be expressed
mathematically by a sum of terms, each of which has the form
A sin {27rmt + c), and therefore corresponds to a simple pendulum-
like oscillation of the particles of air. In this expression, A and
c are dependent upon the value of m, and m assumes successively
the values n, 2n, 3n, 4n, &c., where n, as before, denotes the
number of simple periods in a second.
Now in all cases where the nature of the motion of the
sounding body can be theoretically found and mathematically
represented as a sum of such sines, the ear, when due attention
is paid, can really distinguish notes of n, 2n, 3n, &c. oscillations,
although, in all cases in which such a motion of the air is not
actually produced by different sounding bodies, the coexistence of
a number of simple pendulum-like oscillations of the particles of
air is a pure mathematical fiction.
The universality of this perception of distinct notes induced
a celebrated member of this Academy, the late G. S. Ohm, to
propose as a definition of a simple note that which is produced
solely by a simple pendulum-like motion of the air of the form
A sin {27rmt + c) . This definition of a note given by Ohm was
vehemently attacked by Seebeck, who maintained that it was too
narrow, and that the sensation of a single note might also be pro-
duced by a motion of the air which differs considerably in form
from that of a simple pendulum oscillation. I cannot here enter
into a complete refutation of the objections raised by Seebeck,
and must therefore return to the subject on another occasion. I
will only remark that his objections are founded essentially on
the difficulties which we often experience in distinguishing the
higher notes. In fact, in all observations made by the senses
two things must be kept distinct, viz. the immediate sensation
or effect upon the auditory nerves, and the conception which
arises therefrom by a psychical process, and which leads us to
the conviction of the presence of a certain sounding body. In
the immediate sensation the several simple notes may certainly
be distinguished from one another when sufficient attention is
given ; whilst in the mental image they become blended together
into the impression produced upon the ear by the tone of the
sounding body in question. The attention, indeed, generally
requires artificial assistance in order to distinguish the several
Prof. Helmholtz on Vowel Sounds. 83
elements of the compound sensation, — ^just as, for example, spe-
cial methods of observation are requisite in order to convince
ourselves that the apparent solidity of any object at which we
look arises fi'om the coalescence of different pictures presented
to our two eyes.
On this account I formerly proposed to designate by the name
sound {Klang) the whole compound sensation produced by the
motion of the air proceeding from a single sounding body, and
to limit the name note {Ton) to the simple sensation produced
by a simple pendulum-lilcc motion of the air. Accordingly the
sensation of a sound is generally composed of the sensations
of several simple notes. If we limit to sounds all that Seebeck
said in his discussion with Ohm, and to notes the assertions of
Ohm, both these distinguished acousticians are right, and the
assei'tions of both may remain undisturbed side by side.
We will retain this designation throughout, and at the same
time agree to understand by the pitch of a sound the pitch of
the gravest simple note of n oscillations contained therein, i. e.
the pitch of its fundamental or primary note ; all others will be
called incidental or higher notes. I call the note of 2n oscilla-
tions, the octave of the foregoing, the second note ; that of 3n
oscillations the third note, and so on.
The generosity of His Majesty the King of Bavaria having
enabled me to procure the apparatus necessary for my research,
I proposed to examine the consequences of the proposition of
Ohm on the theory of tones [Klanyfarbe). In a physical point
of view, it has long been known that the different forms of the
aerial waves within each single period of oscillation correspond
to what our ear distinguishes as different tones or qualities of
sound. But this hypothesis rested solely upon the fact that
there was no other possible way of explaining such differences
of tone. An experimental verification was requisite, and this is,
perhaps, now supplied by my researches.
In a physiological point of view, a further consequence
could be drawn from the proposition of Ohm. Since all oscil-
lations which do not correspond to the simple motion of a
pendulum produce sensations in which a certain number of
simple notes are distinguishable, sounds of different qualities
whose primary notes have equal pitch, must, to the ear, be
rendered different by the different intensities of the harmonic
incidental notes. Let us leave out of consideration the different
ways in which sounds of different instruments and voices com-
mence and cease, as also the manifold shouting, grating, jarring,
irregular noises which accompany many of them, and which,
properly speaking, ought not to be considered as constituting the
musical part of the sounds, and let us call the ])art of the tone
G2
8 i Prof. Helmhohz on Vowel Sounds.
which docs not depend upon the above-named accidental circum-
stances, the jmisical tone or qualitij of the sound ; the question
then arises, Do musical tones differ only in consequence of the
different intensities of the incidental notes contained therein ?
But in conceiving the form of a wave composed of several
simple waves, it is of importance to consider not only the am-
plitudes of oscillation of the latter, but also the differences of
phase between them and the primary note. We obtain very
different wave-forms when we combine the wave of a primary
note and its first higher octave, according as we allow the maxi-
mum condensation of the primary to coincide with that of the
octave, or with the minimum condensation of the octave, or with
any other intermediate phase. The former question, therefore,
becomes included in the following more special form : Does the
distinction of musical tones depend only upon the perception of
higher notes of different intensities, or does the ear also distinguish
differences of phase ?
This question would be most directly answered by endeavour-
ing at once to produce sounds of different qualities by direct
combinations of simple notes, sucii as can be obtained with
tuning-forks. The several vowels of the German language ap-
peared most appropriate as objects for imitation, for they may
be produced as uniformly continuous musical sounds, and at the
same time be kept nearly, though not quite, free from unmusical
noises.
My apparatus consists of a series of eight tuning-forks, which
correspond to B (in the deepest octave of a bass voice), and to
its harmonic higher notes as far as h^ (in the highest octave of a
soprano), namely to the notes B, b,f^, b^, d^, f<2, as^, and b^. Each
tuning-fork is fastened between the cuds of a horseshoe electro-
magnet and joined to a properly tuned resonant tube. The mouths
of the resonaiit tubes are provided with moveable covers, which
may be removed bj'^ means of threads whose ends are fastened to
a set of pianoforte keys. The tuning-forks are set in motion by
means of intermittent electric currents, which are produced ac-
cording to the principle of Neef's hammer, and whose number per
second is equal to 113, the number of the oscillations per second
of the deepest-toned fork. After overcoming several difficulties,
I succeeded in so arranging the apparatus that, when put into
action, the low humming of the forks could scarcely be heard so
long as all the resonant tubes remained closed; but as soon as
one or more of the resonant tubes were opened by means of the
pianoforte keys, the respective notes became distinctly audible.
The intensity of any note could be easily regulated by opening
the corresponding tube more or less completely.
I combined in the first place the two deepest notes alone, to
Prof. Helmholtz on Vowel Sounds. 8»
these I then added the third, and giadually several others, and
endeavoured to imitate with the voiee tlie sounds thus pro-
duced. Thus I learnt by degrees to imitate the different sounds
of the vowels more or less completely; U, 0, Oe, E were pretty
good and distinct ; I, Ue somewhat less so, for here the whit-
tling of the air through the mouth, to whose different characters
Donder called attention, is comparatively loudest ; A and Ac
were still worse, because here we require the combination of a
great number of notes, the intensity of each of which cannot be
so completely regulated ; for A, in fact, a series of higher notes,
for which I had no forks, were requisite.
It may be remarked that, in general, the vowel-sounds com-
posed by means of tuning-forks arc more similar to those of the
human voice when singing than when sjieaking. In the dry
sound of our ordinary speech another kind of intonation is
chosen, in which tlie primary note is nmch less prominent than
the higher incidental notes and noises; by this means, in fact,
the differences of tone become more evident than they do in sing-
ing, where the primary note becomes more intense, and thus
hides the incidental notes more completely. The artificially pro-
duced vowels bear the strongest resemblance to those which are
heard when we sing those vowels loudly into the interior of a
pianoforte. The following are the particulars of my results : —
The simple prinuu'y note, compared with the compound sounds,
had the tone of U. The vowel is somewhat more distinct when
the primary note is weakly accompanied by the third note.
0 is imitated when the primary note is powerfully accompa-
nied by its higher octave. A very weak accompaniment of the
third and fourth notes is advantageous, though not necessary.
E is especially characterized by the third note, the second
bemg moderately strong. The fourth and fifth may also be
w'eakly sounded.
The transition from 0 to E, therefore, follows from diminish-
ing the second and increasing the third note.
Oe ensues when both these secondary notes are loud.
Ue arises when the primary note is accompanied by a third
note of moderate strength.
For I, the primary note must be weakened, the second, in
comparison with the primary note, must be strong, the third
very weak, the fourth, which is characteristic of this vowel,
must be loud, and the tit'th moderately strong. The weak notes,
such as the third and fifth, may be omitted without causing
any essential change of quality.
For A and Ae, on the contrary, the higher incidental notes
are characteristic ; the second note may be quite omitted, the
third may be weakly given, but the higher notes must be
86 Prof. Helmholtz on Vowel Sounds.
made as prominent as possible, for by the method here era-
ploj'ed the intensity of the highest is but small. For Ae, the
fourth and fifth notes are specially important ; for A, the notes
from the fifth to the seventh. When the third note is com-
pletely omitted, A has a nasal sound.
I must, however, remark that the above-mentioned relations
between the primary and the higher notes refer only to the pitch
of my tuning-forks. The primary note B corresponds nearly to the
pitch of moderately deep male voices when speaking. I have not
yet had time to conclude my researches on vowels at a higher
pitch, for I was not able to pursue the investigation much
further with my incomplete set of tuning-forks. When I made
the former second note b my primary, I had only three appro-
priate higher notes. With these I was able to imitate U, 0, Oe,
E, Ue, and I according to the given rule ; but the absence of the
higher notes rendered my imitation of A and Ae imperfect ; so
that here, as at a lower pitch, the same relation of upper notes
to the primary one appeared to be essential in the imitation of
the vowel. This higher pitch corresponds nearly to that in
which high voices generally speak.
On the other hand, I canied the investigation further by
direct observations on the human voice by means of a special
contrivance, which renders the most inexperienced capable of
distinguishing the incidental notes of every musical sound, — a
problem which formerly could be solved only by long practice
and great attention. I made use of peculiar resonant vessels,
which were applied to the ear itself. The best vessels of this
kind are glass globes with two openings, one of which termi-
nates in a funnel-shaped neck whose end fits into the ear. If
one ear is provided with such a resonant globe whilst the other
is closed, most external notes are very much deadened; those,
however, which correspond to the proper note of the glass globe
(in combination with the hollow of the ear) are heard with ex-
traordinary distinctness. The upper notes of any external sound
which correspond to the note of the glass globe, are now also
increased in intensity. If, for example, a globe is placed to the
ear whose note is /j, and the vowels are sung on B, whose third
note is /,, it will be found that with U, I, Ue, A, and Ae, the
note of the globe is only feebly heard, whilst it becomes very pro-
minent with 0 and Oe, and extremely intense with E. By the
help of such resonant globes a number of acoustical phaenomena,
such as objective resultant notes, the incidental notes and their
beats, which were formerly difficult to investigate, are rendered
easily accessible. The investigation of the human voice, so con-
ducted, confirmed the results which I had obtained with the
tuning-forks when B was the key-note sung upon ; for keys of
Prof. Helmholtz on Vowel Sounds. 87
higher pitch there were shght deviations. It was found that
for the incidental notes of several vowels, certain parts of the
musical scale are peculiarly favourable, so that these notes, fall-
ing in this part of the scale, become stronger than Avhen they
fall in other parts. Thus, for 0, the upper half of the octave above
the lines constitutes such a favourable part of the scale. The third
and fourth higher notes, which are heard distinctly at a low pitch
of the vowel, lie in this part, and are not so prominent when 0
is sung on a higher key. For A, the upper half of the second
octave above the lines is favourable. The second, third, and fourth
notes, which are weak at the low pitch of the vowel, are very pro-
minent when A is sung between b and 6,. ]\Ioreover, I found
by means of the above-described resonant globes that, especially
for A, there are feeble but audible notes higher than any to
which my tuniug-forks reach. When the vowel A was sung on
F, another globe, which was tuned to es^, corresponding to four-
teen times as many oscillations as F, resounded considerably.
With respect to differences of phase, no effect of the kind
manifested itself in my experiments. I was able to control the
phases of oscillation according to the optical method of Lissajou.
In the first place, by reversing the electrical currents in the
electro-magnet of every single tuning-fork, the oscillation of
the latter can be changed by half an undulation, so that the
maximum and minimum deflections change places with each
other. Further, by fixing a little wax to them, the tuning-forks
can be slightly untuned ; their oscillations then become weaker,
and thus, up to a quarter of an undulation, the phases can be the
more displaced the greater the discordance of the tuning-forks.
The change of phase in the weaker notes may be still more
easily effected. To do so, they may either be weakened by
removing the forks further from the resonant tubes, whereby
the phases of the oscillations of the air are not changed, or the
resonant tubes may be only partially opened ; in the latter case
a change of phase takes place, as I have shown in a theoretical
memoir on Acoustic Oscillations, which is now being printed in
Crelle's Journal (vol. Ivii.). The changes of phase produced in
any one of these ways, however, cause no change in the tone,
provided the intensities of the notes remain the same ; so that the
former question may in general be answered thus : The musical
tone depends only upon the presence and intensity of the incidental
notes in the sound, and not upon their differences of phase.
I must, however, remark that there are apparent exceptions to
this rule. When the notes are sufficiently strong, resultant
notes may become intermixed, which, according to the differences
of phase, may partly weaken and partly strengthen the primaiy
notes, so as to give rise to differences of tone. Here, however.
88 Prof. Cliallis on a Theory of Molecular Forces.
amongst other experimental results, I believe I may venture to
assert that the differences of sound depend only upon the differ-
ences in the intensities of the notes ; but that the latter, under
the above-mentioned circumstances, depend upon differences of
phase.
For the present, however, I would prefer to limit the above
assertion to the lower incidental notes, which, lying far apart in
the scale, reach as far as the sixth and seventh. The higher
incidental notes give discords and beats with each other; and
when a number of such pairs of notes which give rise to beats
are heard together, it is probably not indifferent, as far as per-
ception is concerned, whether the pauses of all these beats fall
together or not. The latter, however, depend upon the differ-
ences of the phase. Moreover, I hold it to be probable that all
these higher dissonant iucidentah notes form what the ear recog-
nizes as accompanying noises, which latter we have already ex-
cluded from our consideration of musical tones.
I have in another place been led to the hypothesis, that each
nervous fibre of the auditory nerve is destined for the perception
of notes of a particular pitch, and is excited when the note which
strikes the ear corresponds in pitch to that of the elastic forma-
tion* in connexion with the fibre. According to this, the percep-
tion of different tones would reduce itself to the simultaneous
excitation of the fibre which corresponds to the primary note,
and of certain others corresponding to the incidental notes.
This simple explanation could not have been given had the dif-
ferences of phase of the lower incidental notes entered into con-
sideration.
XIII. A Theory of Molecular Forces.
By Professor CHALLisf-
THE general Theory of Physical Forces, the principles of which
I have indicated in previous communications, must, if it
have a real foundation, include a theory of molecular forces ; that
is, of the forces by which the constituent atoms of bodies are
held in dififerent states of aggregation — as the solid, the fluid, and
the gaseous. The inquiry into the laws and modes of action of
this class of forces has long engaged the attention of physicists,
and has given rise to a great variety of special hypotheses, mostly
of an arbitrary kind, and not referable to any general principle.
The theory I am about to explain differs from all that have pre-
ceded it in this respect, that it admits of no other kind of action
than the pressure of a very elastic fluid medium (the sether), and
* " Des Cortischen Organs oder Bor^ste in den Ampullen."
t Communicated by the Author.
Prof. Cballis on a Theory of Molecular Forces. 89
no law of force which is not a mathematical deduction, by means
of hydrodynamical equations, from the assumed dynamical jjro-
perty of the medium that its pressure is proportional to its den-
sity. The history of physical science seems to show that theo-
retical investigation proceeds in but one course, that of deducing
quantitative laws, by means of solutions of equations, from
known or hypothetical principles. For example, by the solu-
tions of the first order of differential equations, the law of vis
viva is deduced from dynamical principles known by experiment,
and from D^Alembert^s principle. By the same class of equa-
tions, Kepler's laws are readily deduced from certain hypotheses
respecting the force of gravity. In the latter instance, one of the
hypotheses is, that gravity varies inversely as the square of the
distance from the centre of emanation. As this hypothesis may
also be called a quantitative law, it may, according to these views,
be presumed to be itself deducible from ulterior principles by
means of a higher order of equations. This is what I have
attempted to do in a communication to the Philosophical Maga-
zine for December 1859.
If this course of investigation applies to one kind of force, it
is reasonable to suppose that it applies to all. It is a matter of
demonstration that a theory of molecular forces cannot be con-
structed on the hypothesis that the forces vary according to some
law of the distance from individual material particles, unless the
law be such that the force changes sign with the distance, so as
to become attractive after being repulsive. But if force be a
virtue resident in the particle, it must at its origin be either
attractive or repulsive, and it seems impossible to conceive how
by emanation to a distance it can change its cpiality. This diffi-
culty, as will be shown, is not encountered in a theory of mole-
cular forces, which deduces their laws from the dynamical action
of an elastic medium.
Again, on the same principles it is not permitted to ascribe to
the ultimate atoms of matter any variable quantitative proper-
ties. Accordingly I assume in tlie following theory, as I have
done heretofore, that, while different atoms may be of different
magnitudes, their magnitudes and forms are constant, and that
all have the same intrinsic inertia. The property of constancy
of form might be otherwise expressed by saying that the atoms
are infinitely hard. Further, I make the more particular hypo-
thesis, that all atoms have the form of a sphere. It would be
contrary to these principles to ascribe to an atom the property
of elasticity, because, from what we know of this property by
experience, it is quantitative, and, being most probably depend-
ent on an ayyreyation of atoms, may admit of explanation by a
complete theory of molecular forces.
90 Prof. Challis on a Theory of Molecular Forces.
To these preliminary remarks I beg to add the expression of
my conviction, that theoretical physics can advance only in such
a course as that above indicated, and that progress will be made
in proportion as the difficulties which attend the application of
partial differential equations to physical questions are overcome.
I do not consider the following theory to be free from such
difficulties.
] . It is an evident consequence of the hypothesis that sub-
stances consist of discrete atoms, that neighbouring atoms are
mutually repellent, for they could not otherwise remain in posi-
tions of equilibrium. This action is the repulsion of heat. It
will not be necessary to show here in what manner such repul-
sion results from the dynamical action of undulations of the
aether, because I have discussed this question in the Mathema-
tical Theory of Heat contained in the Philosophical Magazine for
March 1859, and at present I have nothing better to offer on
this part of the subject. There are, however, some mathematical
considerations, relating equally to repulsive and attractive action,
which may now be appropriately introduced.
In an article on Attractive Forces, contained in the Philoso-
phical Magazine for last November, I have investigated the pres-
sure at any point of the surface of a given atom, due to the
incidence of a given series of waves, on the assumption that, for
the case in which the excursions of the particles of the aether are
large compared to the diameter of the atom, the velocity V along
the surface of the hemisphere on which the waves are incident is
W sin 6, and along the sui'face of the other hemisphere,
W sin 6—q . -^— sin 6 cos 0.
at
In this expression, W is put for m sin ( — he], the velocity
of the setherial particles ; 6 is the angle which the radius to the
point considered makes with the radius drawn in the direction
contrary to that of incidence ; and ^ is a certain constant. These
values of the velocity were deduced in the Philosophical Maga-
zine for December, from a particular solution of the general par-
tial differential equation to terms of the first order, of which P,
or Nap. log p, is the principal variable, viz.
dt^ " 'Kdx^'^'dy'^^ dz')'
ralu
V=Wsin^+(/^W-9 — )sin^cos^;
The following is a more general value of V satisfying the same
solution :
Prof, Challis on a Theory of Molecular Forces. 91
or, differently expressed,
,, . ^ . {'Z'lrbt \ , . ^ . . /27r6/ A
V=msmc'sinl -^- he I +mvsm t7cosc/sin( — he' I,
fjb and §', and by consequence v, being in general functions of m
as well as X., and depending also on the magnitude of the atom.
If the last expression be applied to the velocity along the first
hemispherical surface, v = 0, the velocity impressed by the waves
incident on that surface being Wsin 6. For waves having large
values of X and large excursions of the particles, such as those
which came under consideration in the Theory of Gravity, the
factor /A = 0, because, on account of the small size of the atom,
there is no sensible difference between the velocities along the
surfaces of the first and second hemispheres, excepting that
which was shown to be proportional to -j- , and to be due to the
varying momentum of the fluid which passes the plane separating
the two hemispheres. On the other hand, for waves whose par-
ticles perform excursions very small compared to the diameter of
an atom, q must be very small, because the fluid in contact with
the second hemisphere is disturbed but to a small extent, and the
varying momentum just spoken of has very little effect. In this
case we have very nearly
V=Wsin^(l+yacos^).
Now it is evident that V and W must have the same sign, and
consequently that 1 4-/icos 6 does not change sign. Hence the
limiting value of 6 is the arc whose cosine is , which, if fi be
^ IT
a very large positive quantity, exceeds but little — . Thus the
conditions assumed in the mathematical theory of heat are
satisfied by supposing /x to be very large and q to be very small ;
and the fulfilment of these conditions accounts for the great
energy of calorific repulsion. For as the fluid in contact with
the second hemispherical surface is nearly undisturbed, the
pressure on the other is not counteracted by opposite pressure ;
and as the total effective pressure on the first surface varies nearly
as the square of the radius of the atom, while the quantity of
inert matter of the atom varies as the cube of its radius, it follows
that the expression for the acceleration contains the radius of the
atom in the denominator. Hence atoms of very small size, act-
ing upon each other by the intervention of waves of which the
excursions are very small, mutually repel with a very great force ;
and at the same time, as was shown in the Theory of Heat, the
93 Prof. Challis on a Theory of Molecular Forces.
force varies very rapidly with the distance. We have now to con-
sider how this repulsion is controlled by attraction.
2. Conceive the atoms contained in a spherical surface of
radius R to be centres of undulations propagated from them
equally in all directions, and take any point at a distance D from
the centre of the sphere, such that the straight lines drawn to it
from the atoms are quam proxime parallel. Then r- being a very
small but fixed ratio, let the number of atoms included within
the spherical surface of radius 11 be a very large given number N.
It is conceivable that this number may be so large that the
resultant consecutive values of the condensation at the given
distance D, which must be as often jdus as minus, may be ex-
pressed by one or more circular functions, in which the values
of X are very much larger than those for the component undula-
tions. In fact, as the components may be supposed to have
values of X very nearly consecutive, there will be epochs of
coincidence, or greatest proximity, of their maximum condensa-
tions, and equidistant epochs of coincidence, or greatest proximity,
of their maximum rarefactions. The fixed number N is deter-
mined by the condition, that the resultant of the different series
of waves of the first order propagated from the individual atoms,
becomes at the distance D a series of waves of another order,
analytically expressible like the first by periodic functions. As
the waves of the second order cannot, any more than those of
the first, be regarded as due to a specific disturbance, but as re-
sulting from the mutual action of the parts of the fluid, both
ought, according to the hydrodynamical principles which I
have adopted, to be equally expressed by periodic circular func-
tions.
The eff'ect above described is analogous to what takes place at
the surface of water disturbed within a limited space, it being
observable that, whatever be the mode of disturbance, at a short
distance from it are formed and propagated concentric rings
of alternate depression and elevation, which to all appearance
have continuous boundaries, and are probably the resultant of
subordinate series of waves, which have their origins at innume-
rable points at the place of disturbance.
3. For the sake of distinction, the portion of any given sub-
stance which consists of the fixed number of atoms N, will be
called a molecule, whether the space containing them be cubical
or spherical. If the molecule be of the form of a cube, the
quantity represented by U must be understood to be the
radius of the sphere which has the same solid content as the
cube. First, let the substance be in the state of aggregation
of a solid. Then, the mean interval between the atoms being
Prof. Challis on a Theory of Molecular Forces. 93
p
small, the radius R of a molecule will be small, and as ^ is a
fixed ratio, D will also be comparatively small. Hence, as the
condensation propagated from each atom varies inversely as the
distance, it may be supposed that the resultant condensation and
corresponding velocity of the setherial particles at the distance D
from the centre of the molecule, are so large that the excursions
are large compared to the diameter of an atom. Thus the dynamic
effect of the new order of waves will be an attraction towards the
centre of the molecule. The mathematical investigation of the
amount of this attraction will be the same as that I have given
in the Theory of the Force of Gravity (Numbers of the Phil. Mag.
for November and December 1859) ; and the expression for the
acceleration of any atom will consequently be
^TT^qani^
at a position where the maximum velocity of the waves is m. It
is here to be remarked that, as the value of \ is much smaller
for this class of waves than for those which were supposed to
account for the force of gravity, this molecular attraction will be
much more energetic, for the same value of m, than the attraction
of gravity.
It follows from this I'easoning that the waves propagated from
the atoms of a given molecule have no repulsive action at the
distance D, their dynamic action having merged into that of the
second order of waves. The atomic repulsion due to the part of
the velocity which is \inaccompanicd by condensation, must vanish
at a much less distance than D, on account of its varying in-
versely as the /o?/;7A power of the distance. That due to the
part of the velocity accompanied by condensation vanishes more
slowly, but is at its origin comparatively feeble. In this manner
the theory accounts for the small sphere of activity of the atomic
repulsion.
If we consider apart the dynamic action of the same molecule
at distances much greater than D, the condition that the excur-
sions of the particles of the medium are very large compared to
the diameter of an atom, must at a certain distance cease to be
satisfied; the factor q will continually diminish, and the factor jm
become significant, till the molecular attraction will be changed
to molecular repulsion. But the amount of this repulsion, which
will depend on the relative magnitudes of fj, and q, may be very
much less than the atomic repulsion, and vary much less rapidly
with the distance. Also if we take a spherical space of radius R ,
containing N molecules of N atoms, X being the same fixed
number as before, and suppose the molecules to be of the form
94 Prof. Challis on a Theoin/ of Molecular Forces.
of a cube in order that they may fill the space^ then by the same
reasonins as before, at a distance D'from the centre of the sphere
" R' R . .
such that yT'= p:, the waves of the second order will merge into
waves of the third order. It is to waves of this order that the
force of gravity may be attributed. Also the absorption of the
second order of waves into the third, puts a limit to the sphere
of acti%-ity of the second order of repulsion.
As an illustration of the formation of the waves of the second
order was drawn from what is observed to take place at the
surface of water in consequence of its being disturbed through
a limited extent, so the third order of waves are analogous to the
oceari'Swell, or series of long waves, which have been observed
on shores at great distances from parts of the ocean which have
been agitated by a violent storm.
I have elsewhere made the remark, that even the attraction of
gravitation may, according to these views, be changed by distance
into repulsion, so that neighbouring stars may be repulsive to
each other, while at the same time this repulsion is counteracted
by an attraction resulting in the manner above described from
the composition of the waves propagated from all the other more
distant stars. Thus the final waves may be said to be of the
fourth order, and the masses of stars and planets may be regarded
as molecules relatively to the material system of the universe.
4. The above considerations respecting moLeular forces apply
equally to a mass in a fiuid state, the number of atoms in a given
space being not so different in the fluid and solid states of the
same substance as to render any difference in the reasoning
necessary. But experience shows that the molecular attraction
of a fluid mass is much less powerful than that of the same mass
when solid. This difference, which theoretically corresponds to
a difference in the relative magnitudes of yu, and q, is chiefly ex-
hibited in the difi'erent circumstances of the equilibrium of the
atoms at the boundary of the mass, on which, in fact, the differ-
ence between the solid and fluid states essentially depends. If
we take an atom in the interior of a uniform mass, and regard
only the action of forces having very small spheres of activity,
it is evident that whether the mass be solid or fluid, the repulsions
to which the atom is subject will counteract each other, as will
also the attractions. But the case will be different if the atom
be situated at the boundary of the mass ; for there, to maintain
its equilibrium, the resultant of the attractions must be just equal
and opposite to the resultant of the repulsions. This point I
have considered at length in an article " On Capillary Attraction
and the Molecular Forces of Fluids," communicated to the
Philosophical Magazine for February 1836, on the suppositions
Prof. Challis on a Theory of Molecular Forces. 95
that the atoms are isolated, and that the sphere of activity of
attraction is much larger than that of repulsion. These suppo-
sitions are in accordance with the views now expounded; and the
explanation there given of the conditions of equilibrium of an
atom at the bouudai*y applies in the present theory. The prin-
cipal hypothesis of that explanation is one first admitted by
Poisson, viz. that, within a distance from the bounding surface
very small compared to the radius of activity of the molecular
attraction, there is a rapid increase of density from the sui-face
towards the interior. The effect of such change of density will
be to diminish very much the atomic repulsion on an atom at
the surface, while the molecular attraction, on account of its far
greater sphere of activity, will be unaffected by it. The change
of density must be such that the atomic repulsion at the surface
is reduced to an equality with the molecular attraction, the latter
prevailing beyond the surface.
The conditions of the equilibrium of the atoms situated at and
near the sicrfaces of bodies, bring this molecular theory into
relation with electricity.
The difference between the circumstances of the equilibrium
of the superficial atoms of solids and fluids, on which, as said
above, the difference between the solid and fluid states depends,
consists, according to these views, in the different amounts of the
resultant molecular attractions acting in directions parallel to and
very near the surface, and tending to prevent the separation of
the atoms in those directions. In fluids, as experience teaches,
this is a very feeble force ; in solids it is overcome by cutting, or
hy fracture, resuming its sway in the new surfaces which these
operations produce. Atomic arrangement seems to have much
to do with the energy of this force.
Both solids and fluids offer great resistance to compression
within a smaller space. This resistance is due to the atomic
repulsion, and its energy depends both on the gi'cat amount of
this force, and on its rapid variation with distance.
It is also a matter of experience that, when the parts of a
substance (not fluid) arc separated, in general they strongly
resist being joined together again so as to form a single mass.
This fact may be accounted for if we suppose that the molecular
attraction which acts on the atoms situated at the boundary of
the solid, passes through a phase of repulsion before the waves
to which it is due merge themselves in those that give rise to the
attraction of gravitation. But independently of such repulsion,
it is evident that the gradation of density at the boundaries, being
due to the cause assigned above, must be destroyed before sepa-
rate portions of the same substance can be perfectly united. In
cases in which the union is opposed by no energetic molecular
96 Prof. Challis on a Theory of Molecular Forces.
repulsion, extending, as above stated, to small distances from the
surface, it is conceivable that mere mechanical compression of
fragments together, by'acting in aid of the molecular attraction,
may suffice entirely to get rid of the gradation of density, and
thus to effect a perfect union. The very important and instruct-
ive experiments of Professors Tyndall and Huxley, detailed in
the Transactions of the Royal Society (vol. cxlvii. pp. 329-331),
are actual instances of the production of this effect by crushing
together fragments of ice.
As a theory of forces, of the nature of that which I am advo-
cating, can be expected to be established only by the number
and variety of the explanations of physical phpenomena which it
gives, I take this opportunity of remarking that the foregoing
molecular theory, taken in conjunction with the experiments just
referred to, seems to afford a simple explanation of some of the
phsenomena of ^/ffae;-5. Both from the experiments and from
the theory, it may be inferred that the mutual pressures of the
parts of a glacier are continually tending to obliterate fragmen-
tary composition and make it a continuous whole ; and as, ac-
cording to the theory, the interior of a continuous solid mass is
not different from that of a fluid mass, the glacier has a tendency
to flow. The strength of its rigid casing, on account of the
feeble molecular attraction of ice, not sufficing to keep the parts
in the same relative positions, it flows as a stream, as was experi-
mentally proved by Professor Forbes. The rigid envelopes can
accommodate themselves to this motion only by perpetual cracks
and fissures, longitudinal and transversal, alternating with per-
petual reunions by pressure, or by filtration and congelation.
The same theory of the internal condition of solids and fluids,
accounts for a fact relating to the form of the earth, which other-
wise seems difficult of explanation. What is the reason that
being solid it takes the form which allows of a gi'eat portion of
its surface to be covered to a comparatively small depth with a
fluid ? The answer which the theory gives to this question is,
that the mass of the earth, taken as a whole, must be regarded
as a fluid in the mathematical investigation of its form, and the
rigidity of the superficial crust only accounts for local elevations
and depressions, without having sensible influence on the general
form. The effect of internal pressure would cause the distinction
between solidity and fluidity to cease, probably at no great depth;
and consequently any theoretical investigation which admits a dif-
ference between solid and fluid parts at considerable depths below
the surface, would seem to be inconsistent with the laws of mole-
cular forces. For this reason also the explanation which the
Astronomer Royal has offered of the anomalous deviation of the
plumb-line in India, by making the special hypothesis that under
Prof. Challls on a Theory of Molecular Forces. 07
the Himalaya range a large solid mass is plunged into molten
liquid of greater specific gravity, is liable to objection, unless it can
be shown that the distinction between the solid and fluid states,
and any difference of density, can exist under the pressure of
the mountain mass, at the depth wliich the explanation requires.
I have suggested a different explanation of the anomaly in the
article on the Force of Gravity.
If this theory of the internal molecular condition of solids be
true, there must be limits to the heights and acclivities of moun-
tains, and to the depths of ocean-basins, depending on the
energy of the superficial molecular attraction. The separation
of large masses into parts by faults and fissures, by increasing
the quantity of containing surfaces, probably renders a greater
amount of superficial irregularity possible. If these irregu-
larities and the effect of centrifugal force be disregarded, large
bodies, like the sun and planets, would, according to the theory,
take the form of a sphere. The form of a very thin plate, like
that of Saturn's Rings, is also consistent with the theory : but
it does not appear that any form very unlike these two would be
possible.
5. Passing now to the consideration of the gaseous state of a
substance, the first remark to make is, that since the mean
interval between the atoms is much larger than in solids and
fluids, the atomic repulsion, which varies very rapidly with di-
stance, may be supposed to be of insensible magnitude. Also
the condensations and rarefactions of the waves propagated from
a single atom, so far as they are dependent on the number of
atoms in a given space, will be much diminished in the aeriform
state. At the same time the radius R of the spherical surface
which includes the fixed number of atoms X, must be much
greater, and the distance D at which the waves from the atoms
merge into waves of the second order be proportionally in-
creased. Hence the condensation and velocity in the waves of
this order originating in the molecule of radius R, may never
rise to such a magnitude as to satisfy the condition of producing
excursions of the atherial particles large compared to the dia-
meter of an atom. Consequently they will be throughout waves
of repulsion, until they merge into those which act as gravity.
The tendency of aeriform substances to expand is in this manner
accounted for by the theory.
By the aid of this theory, it is also conceivable that a gas, by
being greatly compressed, so that its atoms are brought into
such proximity that molecular atlractiun begins to act, may be
converted into a liquid. Another property of gases is also simply
explained by the theory, viz. the facility with which the atoms
of one gas permeate another. Tiie comparatively large intervals
Phil. May. S. 4. Vol. 19. No. V2o. Feb. 18G0. H
98 Prof. Challis on a Theory of Molecular Forces,
between the atoms of a gas, would allow any diffusive action
operating on the atoms of another gas, to take effect in the
space occupied by the former, and all collision between the two
sets of atoms would be prevented by the proper repulsions of
the individual atoms. It is evident that the force by which the
atoms in motion are diffused, must act on the atoms of the
medium in which the diffusion takes place ; but this action only
produces a slight alteration of the density of the latter, without
affecting its state of equilibrium.
In applying the general expression for the velocity { V) of the
fether along the surface of an atom, to account for the repulsive
force of gases, it must in general be supposed that each of the
constants /x and q has a sensible value, and consequently that
both the hemispherical surfaces of the atom are pressed by the
incident series of waves, the pressm-e on that which directly
receives the waves predominating. This may account for the
comparatively small repiJsive action of a gaseous body which is
at no part extremely rare, such as the earth's atmosphere, at the
upper boundary of which the force of the earth's gravity im-
poses a limit on its rarefaction. But the repulsion will assume
a different character in a gaseous substance of very large extent
and great tenuity, such as was the coma of Donati's comet,
which produced no sensible refraction of the light from stars,
whatever were the direction and length of the path of the light
through it. In this case the dimensions of II and D are greatly
extended; fju becomes large and q very small for waves of the
second order, and their action on any atom approximates to that
of the repulsion of the first order, extending but little beyond
the hemispherical surface on which they are directly incident,
while at the same time the action varies but slowly with distance.
This will account for the enormous development of repulsive
action in the extremely attenuated tails of comets.
6. The foregoing theory of molecular forces admits also of
application to the following physical problems.
Problem I. To account for the difference of elasticity of
different simple gases.
The theory allows of no other difference between simple gases
than a difference in the magnitudes of the component atoms.
Take a portion of one gas bounded by a spherical surface, and
containing a certain number (?t) of atoms, and a portion of the
other gas, bounded by an equal spherical surface, and containing
the same number of atoms similarly arranged. Let II be the
radius of an atom of the former, and r the radius of an atom of
the other, and suppose R to be greater than r. Now by the
theoiy, the elasticities of the gases depend on the waves accom-
panied by condensations which are reflected from the atoms ; and
Prof. Challis on a Theory of Molecular Forces. 99
by hydrodynamics, the reflected condensations, the incident
waves being the same, vary as the radii of the atoms. Hence
the condensations at the same distances from the centres of the
atoms are proportional to the squares of the radii. Hence also
the resultant condensations from all the atoms at points P simi-
larly situated with respect to the two spherical spaces, vary as
the squares of the radii. Let now the number of atoms in that
space which contains the smaller atoms be increased till it con-
tains the same quantity of matter as the other space. Then the
number of the smaller atoms will be — g- , and the resultant con-
densation at P of the waves propagated from them will be in-
creased in the same ratio. Hence the ratio of the resultant con-
densations due to the smaller atoms to the resultant condensations
. R^ r^ R
similarly due to the larger atoms will be —^ x ^r^, or — • And
r xv r
as, according to the theory, the forces which tend to produce
motions of translation of the atoms, to which the pressures
which counteract the expansions of the gases may be assumed to
be proportional, vary as the squares of the condensations or velo-
cities of the incident waves, it follows that the jjressures of equal
weights of two simple gases contained in equal spaces vary inversely
as the squares of the radii of their atoms. Hence the elasticity
of a simple gas is greater the smaller its atoms.
Problem II. To find the relation between pressure and density
in different substances.
This question, which is the special subject of a communication
to the Philosophical Magazine for June 1859, is introduced here
for the purpose of answering it more completely by the applica-
tion of the theory of molecular forces contained in the present
communication. I see no reason to modify the argument by
which the effective acceleration of an atom, due to the action of
the surrounding atoms, may be expressed by the function
H ^
As'
A/0 being the increment of density corresponding to the linear
increment A^ in the direction perpendicular to a surface of equal
density, and therefore in the direction of the molecular accelera-
tion. But it is to be observed that the factor H was obtained
on the hypothesis that the sphere of molecular activity is not
altered by change of density. According to the theory now
advanced, it appears that, while upon an increase of density the
action of the atoms in a given elementary space upon an atom
at a given distance is increased in the same proportion, the sphere
of molecular activity is diminished in that proportion, the linear
H2
100 Prof. Challis on a Theory of Molecular Forces.
quantities ou which the law of moleculai* action depends retain-
ing the same ratios. It follows that the number of the given
elementary spaces containing effective atoms is diminished in
proportion as the density is increased, and consequently that the
factor H is of the form — , the quantity — being given. It is
here supposed that atoms situated in parts of the fluid which
have different densities have the same specific heat, that is, are
centres of waves of equal condensation. But though this is ap-
proximately true in aeriform bodies, it cannot be exactly true,
because, while the waves reflected from a given atom are chiefly
due to incident waves from extraneous sources, they are partly
due to secondary incident waves originating at the surrounding
atoms, and therefore partly depend on the density. Hence, the
reflected waves from extraneous sources being supposed to be the
same throughout the fluid mass, we ought in the place of K to
put KCi -{- a .f{p) J , X being very small. Consequently if G be
the accelerative force which counteracts the molecular accelera-
tion of a given atom, we shall have
and
dp=GpAz = K(l+u.f{p))Ap,
which is the law for gases.
Exactly the same kind of reasoning applies to fluids and solids,
excepting that in these the condensations of the waves propa-
gated from a given atom appear to be determined as to quantity
by the reflexions of successive orders of secondary waves from
the surrounding atoms. It would be in accordance with hydro-
dynamical principles to say that the dynamic effect of waves
coming originally from extraneous sources (as the sun, the pla-
nets, and stars) is by these reflexions multiplied in a certain pro-
portion to the density of the substance. Also among the primary
waves to which the secondary waves are owing may be reckoned
the waves of the second order previously considered, the conden-
sations of which are proportional to the same density. Without
at present discussing this point at greater length, I shall assume
as an hypothesis that the calorific repulsion of solids and fluids is
fully taken into account by supposing that II = \\p. Consequently
Hence
G=^.^ andrfy^ = GpA~=KpAp.
P=^.p^-^C.
Prof. Challis on a Theory of Molecular Forces. 101
Problem III. To find the law of density in the interior of the
earth.
This question is here considered for the purpose of testing the
formula just obtained for the relation between the pressure and
the density in solids and fluids, which is in a great degree hypo-
thetical. To adapt the formula to the circumstances of the earth,
supposed to be of homogeneous material throughout its interior,
let
S being the density of primitive rock, as granite, at the surface.
Then, as is well known, this equation gives for the law^ of den-
sity in the earth's interior, the form being supposed spherical,
p _ sin Qr
p* being the density at the distance r from the centre, D the
density at the centre, and Q a certain constant. If c be the
earth's radius, M its mass, and g the usual measure of gravity
at the surface, the value of the constant Q is given by the
equation
^ - ~MF •
Now since the assumed relation between p and p takes into
account the effect of heat in the earth's interior, the constant k^
has the same value for the whole of the mass, supposed to be of
uniform material. Hence its value maybe found experimentally
by determining the compressibility of primitive rock at the
earth's surface, or, what is equivalent, ascertaining the velocity
with which it transmits sound. (See on this subject an article
" On the Ellipticity of the Planets," which I communicated to
the Philosophical Magazine for September 1831, p. 200.) If
this velocity be called V, by a known process we shall have
^ -X-
Hence supposing the mean density of the earth to be nB, we
obtain for calculating Qc the equation
Qc
The value of n deduced from the law of density is 242. I am
not acquainted with any experimental determination of the value
of V for primitive rock. In art. 1 1 1 of the " Treatise on Sound"
in the Encyclopedia Metrapolitana, experiments which appear to
be trustworthy are adduced which give for the velocity of sound
103 Prof. Cavalleri om a New Seismometer.
in cast iron 1 1090 feet per second. Making vise of this deter-
mination for want of one more appropriate to the problem, and
taking c=3956 miles, it will be found that Qc = 2,602. This
result comes very close to the value -^or 2,618, which has been
assumed in the Theory of the Earth^s Figure solely on the a pos-
teriori ground that it gives results in accordance with the observed
values of the earth's cllipticity and the precession of the equi-
noxes. I have gone through the above investigation chiefly for
the purpose of making the remark, that the assumed relation
between the density and pressure, and the consequent law of the
earth's density, will in a great degree be shown to be physical
facts, if they bear the test of at once satisfying the observed
values of the ellipticity, the precession of the equinoxes, and the
rate of transmission of vibrations through the substance of the
earth's crust. In the same degree, a theory of molecular forces
from which that relation may be antecedently deduced receives
confirmation.
If it may be concluded from the foregoing arguments and ap-
plications of the results, that the theory of molecular forces here
proposed has a real foundation, what will be chiefly required to
complete it is to ascertain by analysis the precise composition of
the functions fju and q which have been so frequently referred to.
Cambridge Observatory,
January 18, 1860.
XIV. Description of a New Seismometer' constructed in the Col-
lege at Monza. By P. G. M. Cavalleri, Professor of Physics
at the Barnabite College of Monza^.
[With a Plate.]
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
THE following memoir by Prof. Cavalleri of Monza, although
in some respects behind the actual state of knowledge,
may not be unacceptable to English readers interested in seis-
mology. From the unfortunate condition of Italy, the learned
of that country know commonly but little of what is doing
elsewhere in science; and our English libraries are miserably
supplied with Italian periodical literature. Hence in 1858,
when in the " Fourth Report on Earthquakes " (Trans. Brit.
Association) I enumerated and discussed all the seismometers
* Published at Milan, February 1858. Extracted from the Atii dell' I.
R. Instituto di Scienze, Lift, ed Arti, vol. i. part 2.
mtMi,. Ser.4.Vol.l9i«/. ^
+-r^ r'-'-V — ^ i.
Prof. Cavalleri on a New Seismometer. 103
known to me, those of Cavalleri I had not heard of, nor yet
until recently I was indebted to M. Jeitelles of Kaschau in
Hungary for a copy of the memoir. I have deemed it worthy of
translation, partly as my amende to the autlior for my uninten-
tional omission of him, and also from the fact that one of his
arrangements, viz. the pendulums of variable length, is I believe
new, and that he places some views relative to the movements of
earth-waves in a clearer light to unmathematical readers than is
usual.
I shall, with your permission, in a future Number of the Ma-
gazine make some remarks as to the limits of utility of the pro-
posed instruments, derived from the experience of the actual
phaenomena of shock, obtained in my observation of the earth-
quake regions of the Two Sicilies early in 1858.
I am, Gentlemen, yours, &c.,
Monkstown, Co. Dublin, RoBERT Mallet.
January 12, 1860.
Physical science, and geology especially, have long sought for
a seismometer which should record the shocks and convulsions
to which the surface of our globe is subject. The various theories
which have been formed on the origin of earthquakes, and the
nature of the strata beneath us, are founded on the various
anomalies and particular effects which earthquakes produce in
different localities. With the increase of data we have ascei'tained
many things relating to physics and geology, many ideas have
been rectified, and many new ones introduced. We have, indeed,
several recent works which show a real advance and true scien-
tific conquest. From the researches of Professor Alfonso Favre,
made known to us in his two recent works on a hundred earth-
quakes which occurred in various parts of the world during the
years 1855 and 1856, not to enumerate other works on the earth-
quakes of Calabria and Tuscany, it is evident that much light
has been thrown on the nature of the waves of the terrestrial
crust when agitated by earthquakes, on their variable rapidity
and intensity according to the difference of the ground, on their
refraction and interferences, on their inclination to extend along
valleys, and in the direction of mountain chains rather than
across them, and on many other questions no less new than
interesting. But these ideas and views need much diligent in-
vestigation before any theory can be formed; and instruments of
measurement are indispensable.
Although seismometers may afford us some facility for the
advancement of science, and may aid in the investigation of these
difficult questions, yet many, despairing of their success, have
affirmed that the direct study of the phsenomena of the earth-
104 Prof. Cavalleri on a New Seismometer.
quake, as exhibited in the effects which it has produced, is a far
superior method. But besides the difficulty of giving, among a
mass of effects apparently contradictory, the due value to each,
we should remember that frequently the earthquake leaves no
distinct trace of direction, origin, or intensity, and still more
frequently no trace whatever. And yet these weak and disre-
garded perturbations might afford precious data to science. The
study of seismometers appears to me very useful, if it be possible
to add anything to what we have already done. A perfect
seismometer should record the traces of the various motions
which affect the surface of the earth, at once marking their com-
mencement, duration, and relati^■e intensity. The formation of
one seismometer which should embrace these complex phseno-
mena being almost impossible, I perceived at the beginning of
my work that it was necessary to divide them into their com-
ponent parts. Such a division being made, the invention of an
instrument which should record these components, or we might
say elements of the complex motion, became much easier. I am
not unacquainted with the many seismometers made and pro-
posed by others, and have endeavoured to profit by their designs ;
but, none appearing to me satisfactory, I have changed and added
to their plans. I subjoin a description of the apparatus which I
have constructed and recently tried.
A brass ball, weighing 3 kilogrammes, is vertically suspended
by a wire 1 millim. in diameter; this wire, in length 1"25 metre,
is fastened at the point of suspension to the end of a strong
iron plate by means of a screw; the plate is secured in the wall,
and projects horizontally from it 5*3 decimetres. A needle is
firmly attached to the lower part of the ball with the point turned
down and finely sharpened ; in length it is 9 centimetres. The
apparatus is in fact a pendulum. The extreme point of the needle
is inserted a millimetre or a little more into an extremely small
cylinder or square prism (viera), but so as to be quite free. This
cylinder rests lightly on the summit of a small support or vertical
column fixed in the centre of an iron pan which is firmly attached
to the wall. The pan is filled with finely-sifted ashes or brickdust
to the level of the needle's point, or a little higher, as may be seen
in the accompanying Plate (PI. I.). The apparatus being arranged
in this manner, it is evident that if a shock occurs, let us sup-
pose from the south, the ball of the pendulum, owing to its own
inertia and the time necessary to transmit the motion from the
top of the wire to the ball itself, will remain unmoved ; while the
wall, the fixed plate which holds the pendulum, the pan, and
the support of the small cylinder will be pushed at the same
instant towards the north. By the simultaneous motion of all
the rigid parts of the apparatus, the support of the vertical
Prof. Cavallcri on a New Seismometer. 105
column is withdrawn from beneath the small cylinder, which is
retained in its position by the point of the needle ; wanting; the
support, it will immediately fall into the soft ashes, pi'ecisely in
the direction from which the lirst shock came, that is, from the
south. This is the first effect of the seismometer, it will indi-
cate the point from which the first shock came. The shock
might occasion a very small movement ; yet as we have the power
of making the point extremely fine, and the cylinder and its sup-
port extremely small in diameter, it is evident that the slightest
shocks would aflfect them, even those of two millimetres or less.
From the experience of others, and from what has come under
my own observation, it is certain that the shocks, although very
weak, would cause a greater deviation than two or three milli-
metres. It may also be urged that the percussion occasioned
by the passing of cars, or by thunder, might be capable of
shaking the walls, and thus giving a fallacious indication of an
earthquake. To this objection I beg leave to reply, that if the
walls of the building be firm, and especially if the instrument be
erected on the ground floor, these extraneous percussions can
have no sensible influence on the walls, but are limited to the
air, the window-panes, and such elastic and moveable objects
as are placed between compressed and compressing air. Although
passing wheels may communicate a motion to walls to which we
may apply the word perceptible, it is in reality very slight, and
almost invisible to the naked eye. For this reason I am led to
believe that the instrument will not be in the least affected by
passing cars, and will sufficiently answer our purpose.
I shall venture to dwell a little longer on this point, and allude
to everything which may possibly influence our seismometer.
Shocks of earthquake, however complicated, and as yet not sub-
mitted to measurement, may be distinguished, as is usually done,
into undulatory and horizontal, subsultatory and vertical, and
mixed shocks, the last being by far the most frequent. The appa-
ratus which I shall attempt to describe will enable us to distinguish
these three kinds of earth-waves. But there is still a question re-
lative to the record of the direction of the primary wave by means
of the small cylinder or prism. When a shock occurs in any given
point of the globe, or rather when the centre of the earthquake is
manifested in any given point, we know that undulations proceed
from that point as from a centre, and aie ])ropagated over a cir-
cumference more or less extensive, according to the intensity of
the shock or the conducting power of the ground. Now I would
ask if the first wave, which is gradually extended and enlarged in
its course, always proceeds from the centre of convulsion to the
circumference, or whether the reverse can ever happen ';' Let us
niaginc the sudden crushing of a large hollow glass ball from
106 Prof. Cavalleri on a New Seismometer.
which the air has been exhausted ; is it not evident that, at the
moment of rupture, the surrounding air will rush violently in to fill
the vacuum, and the first wave will come from the circumference
to the centre; and that the same may be affirmed of the other more
distant waves which successively enter the ball ? On the other
hand, should a certain quantity of gunpowder be ignited, in con-
sequence of which a gas is formed which demands a new or
greater space, will not the first wave proceed from the centre to
the circumference ? To make use of a better expression, we may
call this last wave positive, and the first negative. This ques-
tion might be theoretically treated by mathematicians, and their
considerations might be of essential service in throwing light on
the still obscure origin of earthquakes.
An earthquake may be produced from two very different causes
with reference to our mode of considering the wave. It may
happen that a considerable quantity of water or other matter
may instantaneously produce such a volume of gas or vapour as
will raise or displace in some manner a portion of the terrestrial
crust and afterwards allow it to return to its primitive position ;
on this supposition the first wave must be positive. But if the
steam or gas be slowly formed and expanded gradually (with in-
creasing tension) till it finds instantaneous vent in the open cre-
vices of the earth^s crust, the first wave must be negative. In
either case, laying aside the theoretical consideration of the ever
difficult problem of the waves, of which we know neither the
origin nor the depth, nor the medium through which they are
propagated, nor the great and various pressure of the different
strata, our pendulum may solve the practical question for us ;
for should we find, after a certain number of earthquakes of
which the centre of effort has been subsequently ascertained,
that our little cylinder had been displaced either in the direction
of that centre or in the opposite direction, we might infer whether
the earthquake had originated from the fii'st or from the second
of the supposed causes. Besides, we may conclude that the ne-
gative wave must rapidly decrease in strength as it is removed
from the centre, and cannot be sensibly felt as far as the posi-
tive wave, which is in its nature much more powerful. Some
experiments, although veiy imperfect, which were tried on the
surface of a lake on which were placed wood floats, bearing card
cylinders balanced so as to fall easily at the agitation of the water
either in a positive or a negative sense, led me to conclude that
the negative wave must be extremely weak. The accuracy of
our instrument in noting the direction of the primary wave may
throw greater light on another phenomenon, and perhaps com-
pletely solve it : I mean the phsenomenon already noticed by
some geologists, that the earth-waves produced by shocks take
Prof. Cavalleri on a New Seismometer. 107
certain directions in preference to others, according to the differ-
ent lie of valleys and mountains ; and further, that these waves
are broken in their course and reach a given point more or less
late, thus occasioning confluxes of different waves all generated
from the primary, so as to produce shocks more considerable than
at spots nearer the first convulsion. This appears to be the ne-
cessary consequence of the heterogeneous material of which the
crust of our globe is composed. A single strong shock sent
through strata of different density, arrangement, and elasticity,
the strata also lying at angles widely varying from the direction
of the primary impulse, and afterwards subject to different
changes of dip {incidenza) , must indubitably occasion — 1st, a
composition offerees; whence, 2nd, a different direction of waves;
3rdly and lastly, varying velocity in their progress. These effects
would of themselves be greatly complicated, even admitting that
the waves should act only in one plane ; but when we add, as
truth requires, that the waves necessarily act in different planes
according as the earthquakes are generated at a greater or less
depth, and that the waves must radiate or expand, not over a
single surface, but in a mass of three dimensions, every one must
admit that the phsenomena of earth-waves are most complicated,
and have a thousand different aspects. Our instrument is capable
of recording these anomalies and others which we are about to
notice.
When an earthquake occurs, the pendulum being disengaged
from the cylinder, which falls in the direction from whence the
first wave proceeded, is set at liberty, and traces in the ashes
which lie beneath, and which rise a little above the point, the
general direction of the wave. The application of the pendulum to
tracing the direction of the earth-wave is already known, and has
been frequently tried ; I cannot boast of adding anything further
to this invention than a most important auxiliary. But here
some observations present themselves which I consider very im-
portant. The traces which the ])endulum leaves impressed in
the ashes, as 1 observed at Bologna during the earthquake which
occurred there last year, are in general more or less long and well
marked. These are not occasioned by the oscillations of the
pendulum itself, which are always relatively small, but by the
ground moving under the pendulum. The pendulum is soon set
in motion, but its oscillations arc very limited, and take the form
of ellipses, — at first very excentric, almost pointed; but they
shortly lose their excentricity and increasetheirminor axes, until
they become small circles. These figures are easily perceived
if the point of the needle is sharp, and the ashes or brickdust
smooth and regular, but only when the earth-wave proceeds from
one direction. Should the waves come from two or more, it would
108 Prof. Cavallcri on a New Seismometei\
be impossible to make them out accurate!}'. However, if we can-
not always accurately tell the direction of the waves which have
ditferent horizontal inclinations, we can at least discover the
direction of the principal one. Since the oscillations of the pen-
dulum, especially if it be a long one, must be very small in com-
parison to the motion of the terrestrial crust lying beneath it,
we hope no argument will be drawn thence against increasing
the sphere of application of our seismometer. Another desi-
deratum is to mark the time when the earthquake commences.
In some seismometers which I saw at Bologna, and in others of
which I have read, at the moment the shock occurs, the pendulum
liberates a rod or a weight which in some manner (several me-
thods are employed) stops the motion of a timepiece which is
placed near. In others, a pencil moved by clockwork draws a line
on a card divided into twenty-four parts, according to the hours of
the day ; an irregularity in the line will prove the occurrence of an
earthquake. This manner of marking time has the advantage of
compelling the observer to take daily note whether an earthquake
has occurred or not ; but is attended with the enormous incon-
venience of requiring a person to attend to the instrument daily,
perhaps for years, before the occurrence of the desired phseno-
menon. In our apparatus it is just the reverse. The timepiece,
constructed with a main spring and a sti'ong balance, and secured
to the wall, is always wound up, but does not go. The instant
a shock moves the pendulum, however slightly, a lever which
retains the balance in a position favourable to its easy disengage-
ment, is set at liberty, and the timepiece begins to mark time.
The index is placed at zero, and can mark twenty-four hours, the
dial being divided into twenty-four parts. It is evident that at what-
ever hour of the twenty-four a person perceives the motion of the
clock or the displacement of the lever, or hears the ticking of the
timepiece, &c., he can accurately tell at what hour the earthquake
took place, by subtracting from the true time, as given by chro-
nometers, the hours recorded by that which is attached to the
seismometer. A whole day could not possibly elapse without
the attention of some individual being attracted to the instru-
ment, especially if (secured in a glass case) it were erected in a
frequented and easily accessible place.
But seismometers ought to mark not only undulatory or hori-
zontal motions, but subsultatory or vertical also, as well as mixed
ones. With regard to vertical upheavals, I have made use of a
property which I observed belonged to spirals or elastic coils
{cliche), viz. their power of vertical oscillation. I reflected that
as the oscillations of the pendulum mark in a horizontal direc-
tion the horizontal undulations of the ground, so the vertical
oscillations of the spiral might mark the vertical elevations of
Prof. Cavalleri on a New Seismometer, 109
the earth's crust. Let us imagine a spiral formed by an iron
wire, hard as from the draw plate, with rings of equal size, form-
ing a cylinder the spires of which are separated from each other.
Let the spiral be attached at one extremity to a fixed point, sus-
pended with its axis vertical, and let a moderate weight be placed
at the other extremity. The spiral will lengthen and stretch a
little, and then remain motionless. Now if the weight be pushed
up and then left free, the spiral will oscillate like a common pen-
dulum, only vertically. The elasticity of the spiral performs the
same office as attraction in common pendulums. The descend-
ing weight acquires an accelerated motion, which tends to stretch
the spiral more than it would do were it at rest ; hence follows
the reaction of the elastic spiral, which tends to draw the weight
up more than it would do were it motionless ; and this continues
until, after a certain time, the resistance of the air and the im-
perfect elasticity of the spiral stop the vertical pendulum. Such
is the apparatus which I have constructed for noting vertical up-
heavals or elevations of the earth's crust. But as the number
of the oscillations of the spiral within a given time must depend
on the weight which is attached, the size of the rings or turns,
the thickness of the wire, and the number of the rings, I consi-
dered it necessary to institute a series of experiments in order to
give to the spiral, conditions capable of fultilling our intention,
and thus to render complete a work which, so far as I am aware
of, has not been done by another.
The following laws are the result of my experiments : —
1st. The vertical oscillations are isochronous.
2nd. With the same length of wire, the number of oscillations
in a given time is in the inverse ratio to the diameter of the
spiral.
3rd. The number of oscillations with the same number of
rings is in the inverse ratio to the square root of the weights
which stretch the spirals, subtracting the weight of the spiral
itself, which acts as a weight and tends somewhat to retard the
oscillations.
4th. The number of the oscillations in a given time is in
inverse ratio to the square root of the number of rings or coils
in the spiral.
5th. With the same weight, length of wire, and diameter of
spiral, the number of oscillations is in the inverse ratio to the
diameter of the wire.
The first and fifth of these laws agree fully with those dis-
covered by Coulomb relative to the elasticity of torsion. The
second (note being taken that the spirals used in my experiments
are cylindrical) arises from the constant relation between the
length of the wire and the number of rings in the spiral, and
110 Prof. Cavalleri on a New Seismometer.
must therefore substantially agree with the laws of the samfe
philosopher. The third would agree if the weight of the spiral
were nought, or might be so considered; but as one cannot
attach to the spiral a weight which would render the weight of
the spiral itself evanescent, since it would draw down the spiral too
much and cause it to lose its elasticity, so the weight of the spiral
has always a sensible effect, and tends to retard the oscillations :
some advantage is gained by the use of spirals of tempered steel.
The second law has no counterpart [riscontro) among those of
Coulomb, as it depends on conditions not found in twisted
threads, on which the laws of elasticity of torsion depend. With
the same wire and of the same length, spirals can be formed
which will have widely different oscillations by enlarging or nar-
rowing the diameter of the coils.
These laws ascertained, it is easy to find the conditions best
adapted to our purpose. The weight attached to the spiral must
be of a certain size in order to produce a strong reaction, and to
move the markers which we are about to describe. The oscilla-
tions ought to be slow, so that the time employed by the rising
and falling of the ground may not exceed that required to trans-
mit the motion from the top of the spiral to the weight itself.
I have therefore given to the spiral, measured along its axis, a
length of 80 centims., and attached to it a weight of 1*2 kilog.
The diameter of the cylindrical spiral is 5-3 centims. It con-
sists of ninety rings, and vibrates seconds : the diameter of the
wire is about 3 millims. I have constructed it in the following
manner : — A strong iron bar fixed in the wall supports one end of
the spiral ; a cylindrical weight of equal diameter to the spiral
is attached to the other extremity. This weight oscillates freely
within an iron ring secured to the wall. The spiral is enclosed
in a kind of cylinder in which it can freely oscillate vertically,
but not horizontally. The weight terminates in a point, and
rests on the short arm of a lever very easily moved ; the other
arm of the lever, by means of a graduated quadrant, serves as
an index. All this apparatus of lever, quadrant, and index, is
securely attached to the wall, and is united to the bar by which
the spiral is suspended. Now let us suppose that the ground
has been suddenly elevated by an earthquake. It is evident
that, when the wall and the bar which holds the spiral are raised,
the arm of the lever, being part of the same rigid common system,
will rise also. But for a certain time the weight attached to the
spiral will remain unmoved in its place, because a sensible time
is necessary to communicate motion from the top of the spiral to
the weight itself. Meantime the short arm of the lever will be
pushed by the weight, and being very light, it will fall, while
the longer arm will rise and record the elevation. This arm is
Prof. Cavalleri on a Neio Seismometer. Ill
ratcheted in such a way that it can easily go up, but cannot
descend, as seen in the figure (Plate I.). Thus the index will
mark the elevation of the ground or vertical undulations, the
ratio between the two arms of the lever being taken into account.
Instead of the lever we may use a cylinder of cork a little larger
than the weight, which cylinder must run easily between two
fixed vertical side-pieces or guides, as represented in the figure.
As £ar as the cork, by the push of the weight, has been lowered
it will remain fixed there, being light and held by its own elas-
ticity so fast that it is impossible for a shock alone to move it
from its position. An upright scale, suitably divided, placed at
the side of the cylinder, shows the height of the vertical wave, —
as it rises with the ground, while the cylinder is depressed.
This last method is, I think, superior to that which I constructed
with the lever.
This instrument is so delicate, that by giving, if necessary,
a larger diameter and a greater length to the spiral, and a cor-
responding weight, we may succeed in marking any slight ele-
vation of the soil performed in a relatively long period of time.
For example, we might record an elevation with a velocity of a
millimetre per second, or even still slower. Knowing by obser-
vation that elevations or depressions of the soil occupy a very
short time, I thought it useless to give the spiral a longer time
of oscillation. It may happen that the first vertical wave is one
of depression and not elevation ; but in this case also the instru-
ment will accurately note the vertical movement, in consequence
of the elevation which succeeds the depression. It may happen
also, and in fact often does, that the weight gradually stretches
down the spiral and falls a certain degree (by loss of elasticity,
namely) ; but in this case the short arm of the lever is carried
down also by the weight, and the other arm the place fixes, on
account of the ratcheting already mentioned, so that the space
found between the weight and the lever below it will always
indicate the height of the vertical wave. I will not conceal an
objection which may be alleged against this method of measuring
vertical undulations — an objection which, with much greater rea-
son, may be raised to other seismometers, — viz. that when vertical
undulations are frequently repeated, the instrument will mark
sometimes more and sometimes less than the real altitude of the
earth-waves, according as the time of the undulations is tauto-
chronous with that of the oscillations of the pendulum or the
contrary. If the spiral perform its oscillations more slowly,
this defect will generally be very small ; and besides, these ver-
tical shocks being almost always confined to a single pulse, the
instrument will mark accurately in most instances.
Lastly, there remain mixed shocks, i. e. those which, besides
] 12 Prof. Cavalleri on a Neto Seismometer.
moving the ground with the objects upon it in a horizontal
direction, also elevate or depress it. These waves, which for
perspicuity we have called mixed, are perhaps in reality the only
ones which exist. Several authors, especially geologists, treat of
these waves, — some from one point of view, some from another,
and many so hastily that it may truly be said we are yet far from
possessing a theory of their nature. Such at least is the im-
pression received from the papers of Gay-Lussac, Humboldt,
Achille Rossi, Savi, Colleguo, Pilla, Favre, and more particularly
of Dr. Young, who compares (I use his own words) "the earth-
quake of land to the earthquake of the air.'^ He also compares
the shock to the striking of a number of balls placed in a right
line, of which, when the first is struck, the last only is separated.
We can do no better, therefore, than closely to adhere to obser-
vation, and patiently record the components of these waves in
order to draw deductions from them. In fact, having the ver-
tical altitude of the wave recorded by the spiral, and the hori-
zontal deviation marked by the pendulum, we possess all the
necessary data for mixed waves. Acting thus at right angles
(leaving aside for the present more subtile considerations), we
may regard the mixed wave as the diagonal of these two forces,
so that the mixed wave would be equal to the square root of the
sum of the squares of the abos'c-named components. Besides,
we might also get the inclination which the plane of the mixed
wave makes with the horizon by considering this diagonal as
radius, and the vertical altitude given by the spiral as the sine,
the angle of inclination being that correspondmg to this sine.
A good seismometer ought also to mark the time of the duration
{tempo del/a durata) of the shock ; but although I do not think
it impossible to form such an arrangement as should mark this
also, the pi'oblem appears so complicated and difficult that I am
not at present prepared to attempt its solution. I have rather
sought to discover the time which the earth-wave employs in its
excursion, or that of the seismometrical oscillation. It is desi-
rable to learn how many undulations the earth-wave makes in a
given time, and thence to see if this do not differ in every instance
of earthquake and in every country, on account of the different
strata through which the wave is transmitted, and perhaps also
on account of the diversity of originating causes. Earthquake-
waves, so far as I can remember in three distinct cases which 1
have ])resent to my mind, appeared very rapid and almost iso-
chronous. Recalling these shocks, it does not appear to me far
from the truth to assign about three undulations per second as
the rate, at least in our Lombardy Plains. The instrument
which I have constructed with this view will note the duration
of these undulations, and consequently whether they are different
Prof. Cavallei'i on a Neiv Seismometei'. 1 1 S
in various countries and in different eartlicpialces. The principle
upon wliicli tlie instrument is constructed is very simple.
Let us imagine a pendulum formed by a ball suspended by a
wire, and this wire attached to a moveable point of suspension.
If this point of suspension be moved forward and backward a
certain distance in the same horizontal line, moving to and fro
in equal times with the time of oscillation of the pendulum itself,
then the arc which the pendulum makes continually increases
with the increase of the motion to and fro of the point of sus-
pension. If, however, the motion of this point occur in times
which are not isochronous with the oscillations of the pendulum
itself, its arc of oscillation will become less. In the first case, to
the momentum which the pendulum acquires from being dis-
placed by following the altered perpendicular of the point of
suspension, must be added the momentum communicated by its
moving to and fro, and so the arc of oscillation is increased. In
the other case the force of the moving to and fro is partly or
entirely subtracted from the vibrations of the pendulum, since it
acts more or less in a contrary direction ; hence the arc of vibra-
tion is diminished. A reciprocating motion tautochronous with
the pendulum causes the greatest arc of oscillation. These con-
siderations being premised, I take a strong bar inclined some
degrees towards the horizon. To this bar, and at such distances
as shall exceed the amplitude of the largest earth-wave occurring,
I fasten a number of small pendulums, as represented in the
Plate. These pendulums terminate in sharp needles which touch
the ashes beneath them, so that when a shock occurs they leave
impressed the traces of their vibrations. The ashes are hollowed
out like a cup, in order to assimilate to the arcs traced by the
various pendulums, and prevent the deep impression of the
needles, which might partly hinder their vibrations. The lower
extremities of the pendulums form a horizontal line, as in the
figure, so that their lengths vary : they are ten in number,
which I consider sufficient. I have arranged them in such a
manner that the shortest will make a little more than four oscil-
lations per second, and the longest two. These two limits, of
about four and two oscillations per second, appear to me suffi-
cient to embrace every undulation occasioned by any earthquake.
Let us suj)pose the pendulum to be set in motion by a shock.
All the pendulums will vibrate, and leave separately traces of
their oscillations impressed on the ashes ; and the pendulum
which has marked the largest arc will have performed its oscilla-
tions in equal times ivith those of the earth-wave; so that by find-
ing the square root of the length of the pendulum, or, better, by
actually observing its time of oscillation, we shall learn the dura-
tion of the undulations of that particular shock and in that
Phil. Ma(j, S. 4. Vol. 19. No. 125. Feb. 18G0. I
114 Prof. Cavalleri on a Neio Seismometer.
locality. I must add that usually, if not always, the undulations
are several in number, and therefore the increased force which
the tautochrouous pendulum acquires will always cause it to
make an arc of oscillation visibly larger than the others, so that
no doubt can arise as to which of the pendulums is that accord-
ing with the motion of the earth-wave ; but strictly, a single
tautochrouous wave would be quite sufficient. For clearness, we
have here assumed the terrestrial wave to be horizontal ; usually;
if not always, however, it is mixed, and inclined more or less to
the horizon. However, in this case it is obvious that, if we
separate the mixed wave into its horizontal and vertical compo-
nents, the latter being perpendicular to the horizon, can have no
influence on the arc of oscillation of the pendulum, whilst the
horizontal force remains alone active. The knowledge of the
velocity of earth-waves, besides determining the relative inten-
sity of earthquakes, may lead to most valuable discoveries, and
explain many phsenomena which now excite strong interest. I
think that, having gained this knowledge by the aid of our seis-
mometer, we possess the necessary data for calculating the inten-
sity of the shock or earth-wave. In short, the intensity of the
wave may be represented by three distinct elements; viz. the
vertical altitude which the ground attains, the horizontal lengths
of the wave, and the time occupied by this simultaneous move-
ment. On this supposition, the intensity of the wave may be con-
sidered in the direct ratio of the two first quantities, and in the
inverse ratio of the time. Now our instrument being capable of
marking, 1st, the vertical altitude of the wave by the spiral pen-
dulum ; 2nd, the horizontal undulation by the great pendulum ;
3rd, the time of the wave as marked by one or other of the small
pendulums, we have all the elements necessary for calculating
the intensity of the shock. Lastly, it is clear that with these
three elements we can make all possible theoretical inferences,
and assign to each of the three its appropriate value in referring
to the effects df an earthquake, whether on buildings, on plains,
or on the sea, &c., in all of which one or other of the three men-
tioned powers will have a greater or less influence : it has been
proved, for example, that with an equal degree of intensity, the
vertical shock will do more damage than the horizontal. Thus
we can note with these instruments —
1st. The moment at which the earthquake occurs.
2nd. The direction of the primary shock or earth-wave.
3rd. The general horizontal direction of the waves, their am-
plitude, or length.
4th. The height of the vertical wave of shock, however
complex the vertical and horizontal waves acting together
may be.
Prof. Cavalleri on a New Sej^omefer. 115
. 5th. The resultant of both these eleiiients/or the mixed shock
itself.
6th. The inclination to the horizon of the mixed shock.
7th. The velocity and time of the wave.
8th. The total intensity of the wave, introducing into it the
element of time as furnished by the pendulums.
If, then, as frequently happens, we also know the total dura-
tion of the earthquake, we may approximately infer its total in-
tensity. I say approximately, because it appears that the last
undulations are always weaker than the first or following ones.
Were it not for this, ve might obtain the intensity due to any
given earthquake by multiplying the intensity of one wave, as
above, by the number of the oscillations which were made by the
pendulum in the total time the earthquake lasted. We shall
conclude the description of this apparatus with a remark equally
applicable to the other seismometers, which we purpose briefly
to notice.
In earthquake convulsions, very irregular or rotatory pertur-
bations occasionally occur. Our seismometer, although it is
incapable of noting all, can record the most important of these
convulsions, and intimate the occurrence of others by the irre-
gidar marks wliich will be impressed on the ashes. Lastly,
wherever the centre of effort may be, the ground must be so
affected as to desti'oy the apparatus, if happening to be there
set up. This, however, will not occur once in a thousand times ;
so that out of a thousand instances the instrument will be of
service in 999, as may be seen in the repeated shocks which
occurred in July 1855, at Yispe in the Alps, as observed and
described by Favre.
To complete my remarks on seismometers, it is necessary to
institute a comparison of our seismometer with those that have
come under my notice. Passing over some which do not deserve
the name, such as the vessel of water with jloating particles (una
polrere gaUegyiante) which is spilled by the earthquake, we shall
mention one attributed to Cacciatore, but really invented by a
Milanese, as I was assured by the astronomer Carlini.
The remainder of Professor Cavalleri's memoir is occupied with
a detailed description and discussion of the defects, &c. of the
seismometer of Cacciatore (which he states has received import-
ant improvements by Coulier, but the nature of which Signor
Cavalleri had not learnt) ; of Kreil ; of those suggested by myself
(as extemporaneous instruments only), in the first edition of the
'Admiralty jNlanual/ and of that of Prof. James Forbes.
As these have, however, all been more carefully described, and
12
11(> M. Fittig on Acetone.
their principles and disadvantages pointed out by myself in tlie
discussion of the Seismic Catalogue of the British Association
(" Fourth Report on the Facts and Theory of Earthquakes,"
Trans. Brit. Ass. 1858), it is unnecessary to occupy the English
reader with the conclusion of the memoir, except to give the
explanation by the author of his diagram. — R. ]M.
EXPLANATION OF THE PLATE.
A. Strong iron bar fixed in the wall.
B. ^loveable disc in contact uith the arm of lever.
C. Pan of fine ashes or brickdust.
D. Small cylinder or ])rism (viera) resting on
E. Metallic column fixed to the pan, in order to show the direction of the
primar}- wave.
F. Two arms of a lever, the longest of which rests on the pendulum B,
and the shortest acts as detent to a timepiece to prevent it going.
G. Timepiece with spring and balance always wound up, but not going,
until tlie earthquake moves the small arm of the lever which acts as
detent to the balance.
H. Bar fixed in the wall supporting the spiral.
L "Wire s])iral. marking the vertical motion of the earth -wave.
L. Tube, or guides (re^oZij, which do not allow the spiral to oscillate hori-
zontally, but only vertically.
M. Iron bar fixed in the wall, bearing a ring in which
N. The weight which stretches the spiral can move freely.
O. Lever, the small arm of which is lowered by the vertical undulation,
and the long arm raised ; and on account of the ratcheting it cannot
fall again, and so indicates the height of the vertical wave.
P. Cork cylinder running freely by its own elasticity between two side
guides {refjoli). This cylinder is jdaced under the weight of the
spiral, and being lowered by the motion of the ground or vertical
wave, and remaining where it is driven by the weight, indicates the
height of the vertical wave.
Q. Needle of the large pendulum factual size), with the small cylinder and
part of the little column which supports it.
R. Small pendulums on a graduated scale, as to length, to note the time of
the earth-wave.
XV. Chemical Notices from Foreign Journals. By E. Atkixsox,
Ph.D.,F.C.S., Teacher of Physical Science in Cheltenham College.
[Continued from p. 52. j
FITTIG "f^ has investigated several processes of decomposition
of acetone. AVhen sodium is added to acetone, the liquid
becomes filled with white flakes, and is ultimately converted into
a lustrous, gelatinous substance, without the disengagement of
any permanent gas. On subjecting the mass to distillation, a yel-
lowish viscous oil was obtained which soliditied to a crystalline mass.
This mass, freed by pressure between paper from some adherent
oil, and crystallized from a small quantityof boiling water, yielded
* Lieb^'s Annaleii, .\pril 1859.
M. Fittig on Acetone. 117
large transparent quadratic plates. They contain water of cry-
stallization^ and even by pressing between paper partially lose their
transparency. Their compositionwas found to be C^" H'^ 0^: Fittig
considers that the body is an isomeric modification of acetone, the
rational formula being C'" H^ 0'^ + 6 aq. The crystals gradually
lose water when exposed to the air, and more rapidly in vacuo
over sulphuric acid; but it was impossible to determine this loss
exactly, owing to the volatilization of a portion of the sub-
stance. That the substance was formed from the decomposition
of acetone, and not from the crystallization from water, was
proved by the fact that when some of the crystalline mass was
pressed and crystallized from anhydrous ether, the crystals formed
had the same composition.
Fittig further examined the action of caustic lime on acetone.
Well-burned marble wae covered with acetone, and left in closed
vessels for some time ; tlie dry yellowish mass was then distilled.
On rectifying the distillate, it was found to consist of two bodies,
of which one distilled below 150° and the other above 200°. By
fractionally distilling the first of these a body was obtained which
boiled at 131°*5, and in its analyses and properties was found
to be identical with Kane's oxide of mesityle or mesitic ether,
(3i2jfioQ2^ It is a colourless transparent oil, smelling like pep-
permint, and with a caustic taste. It burns with a lustrous
tUinic, and is not soluble in water, but readily so in ether and
alcohol. Oxide of mesityle is converted into a resin by the action
of nitric acid, and with chlorine it yields a substitution product.
The other body produced by the action of caustic lime, was
found to be partially decomposed by distillation. The analysis
of a specimen gave results agreeing with the formula C'^ H^^ Q-.
Hence it might be formed from 3 atoms of acetone with the eli-
mination of 4 atoms of water. It is isomeric with phorone* ;
and in a subsequent investigation! Fittig found that it was iden-
tical with that substance. The body from acetone, by treatment
with anhydrous phosphoric acid, yielded cumole, C'^ H'-^, from
which, by oxidation with nitric acid, nitrobenzoic acid,
C"'HS(NO^)0^
was obtained, — a result interesting as showing that from acetic
acid, a member of the fatty acid scries, a derivative of benzoic
acid, a member of the aromatic acid series may be obtained.
The action of sulphuric acid and of alkalies on acetone appears
to be identical, giving rise to the formation of a series of bodies
which arc acetone minus water, as is seen from the list.
* Phil. Mag. vol. xiii. p. IBS.
t Licbig's Annalen, December 1859.
118 M. Stadeler on Acetone.
Boiling-
point
Oxide of mcsityle . Ci2Hi0O2 = 2 Acetone-2HO 131°-5
Phorone? . . Ci« H^'* 0^ = 3 Acetone -4H0 210
Mesitylene . . C'^H^^ =3 Acetone -6 HO 155
Xylite Naphtha . C^^ H^^ 0^=4 Acetone- 2 HO 119
Xylite oil . , C^ HIS 0^ = 4 Acetone -6 HO gOO
Chlorine acts on acetone in diffused light with great energy.
The product of the action was washed, dried, and distilled. On
rectification its boiling-point was found to be 120° C. Its
analysis and the determination of its vapour-density give for its
composition the relation C^ H'* CP 0'^, which is that of Kane^s
Mesitchloral. Fittig considers it to be bichlorinated acetone.
That it belongs to the acetone type, is evident from its forming a
ciystalline compound with bisulphite of soda. It is a colourless
liquid with a penetrating odour, and strongly affects the eyes.
It has an extremely caustic action on the skin. It is insoluble
in water, but dissolves in alcohol and ether.
By the action of nitric acid on acetone a heavy yellowish oil
is obtained, which from its ready decomposability and explosive-
ness appears to be a uitro-compound. Its properties precluded
any accurate examination.
Fittig has further * examined the products of the destructive
distillation of acetates. He finds that acetone is not the only
product, but that other allied substances are formed at the same
time. In their separation he found it most convenient to use the
oil which floats on the surface of the crude acetone, in its pre-
paration. He succeeded in isolating the following bodies : —
Methylacetone, C^ H^ 0^, a colourless liquid resembling acetone,
but boiling between 75° and 77°.
Ethylacetone, C'^H^'^O^, a colourless liquid also like acetone,
and boihng between 90° and 95°. Both these bodies form cry-
stallized compounds with bisulphite of soda.
Duinasine. — This substance was first discovered by Kane, who
assigned to it the formula C'^ H^ 0. It is a colourless liquid,
which, however, gradually becomes yellow. It is lighter than, and
insoluble in water, but quite soluble in alcohol. Fittig^s analysis
gives for it the formula C^^ H^° 0"^. It is isomeric with oxide
of mesityle, but is distinguished by forming a crystallized com-
pound with bisulphite of soda, which oxide of mesityle does
not. Dumasine forms a chlorinated substitution product,
C12 H8 Cl-2 02.
Stadelerf has published an investigation of acetone, the greater
part of which consists of the details of experiments the results of
which have been already announced.
* Liebig's Annalen, April 1859. . t Ibid. Sept. 1859.
M. Schwauert on Derivatives of Hippunc Acid. 119
He has examined the body discovered by Fittig ; he prepared
it by the same method, and his description of its properties agrees
with that of Fittig. He finds that, according to the conditions
of its crystalhzation, it forms either long prismatic needles or
thick plates. On account of its property of crystallizing in large
plates, he names it pinakone {iriva^, a plate). Stadeler's analyses
of the body lead to the formula C^^ Hi^O^ + l^HO. He re-
presents it as formed from acetone by the loss of oxygen in the
following manner : —
3(C6H6O2) + 3Na=2NaO + CinP0O2 + 2H
Acetone. Oxide of
mesityle.
2(C«H6 02)+ 2H = 2H0 + Ci^H^^O^
Acetone. Pinakone.
, The soda formed at the same time decomposes some acetone,
producing several oily bodies which distil over with pinakone,
and among which appears to be phorone.
Schwanert* has investigated the action of pentachloride of
phosphorus on hippuric acid. At ordinary temperatures there is
no action; but when the mixture is gently warmed, hydrochloric
acid is evolved, and a liquid distillate is obtained. The decom-
position differs according to the proportions taken. When a
mixture of one atom of hippuric acid with two atoms of penta-
chloride is distilled in small quantities, oxychloride of phosphorus
first passes over, followed by a colourless oily liquid which distils
between 180° — 200''C.; and at length a liquid passes over
between 200° and 250°, which partially crystallizes. In the
retort a solid insoluble mass is left. The distillate between 180°
— 200° consists of chloride of benzoyle, containing a small
quantity of crystals which have the composition C^^ H^ CI NO^ :
the crystals which distil over in the reaction consist chiefly of
this substance. When pure they are colourless prisms, which
fuse at 45°, distil at about 220° C, and crystallize on solidifying.
They are distinguished by their great stability, which renders
their investigation very difficult. Caustic potash is \Nathout
action \xpon them. They form with hydrochloric acid a crystal-
line compound, which readily gives up hydrochloric acid. Besides
this body there is formed in the reaction a small quantity of an-
other crystalline coni])ound, which seems to be C'^ H^CT- NO^.
They are both probably substitution products of a compound,
Ci8H7NO'^.
Anhydrous sulphuric acid acts on hippuric acid, forming a
clear brown solution. This is mixed with water, nearly neutral-
* Liebig's Annalen, October 1859.
120 M. Schiel on Oxidation by Chlorous Acid.
izcd with carbonate of Icad^ filtered, tlie filtrate decomposed with
sulphuretted hydrogen^ and the filtrate from this carefully eva-
porated. A brownish yellow hygroscopic mass remains, which
is sulphohippuric acid. Its formation is thus expressed :
CIS H9 ^Q6^ go ofiz=Cis H9 NS2 012.
Hippuric acid. Sulphohippuric acid.
Sulphohippurate of baryta, formed by treating the carbonate
with the acid, is bibasic, and has the formula
CiHFBa2NS2 0'2 + 2H0.
Sulphohippuric acid is decomposed by nitrous acid into sul-
phobenzoic acid and glycolic acid.
Nitrohippuric acid, Ci^H^(NO'*) XO*^, formed by the action
of sulphuric and nitric acids on hippuric acid, crystallizes in
line white needles. By treatment with sulphuretted hydrogen
this body is converted into a)nidokippuric acid, C^^ H^ (NH^jNO^.
It crystallizes from alcohol in light colourless laminse. It is
difficultly soluble in ether, but readily so in boiling water and
alcohol. Its selutions soon become coloured on standing.
Schiel* has investigated the action of chlorous acid on certain
organic substances. He found that chlorite of lead, which can
be readily procured in large quantities, is a convenient form of
using this reagent. When 30 or 40 grms. of chlorite of lead
were mixed with about two-thirds the weight of alcohol, and a
few drops of sulphuric acid added, the mixture soon became
coloured yellow from chlorous acid; but when exposed to the
sun, this colour disappeared. Sulphuric acid was added from
time to time until the chlorite was quite decomposed : the liquid
product of the reaction was found on rectification to consist of
acetic ether. Its formation may be thus expressed :
if Chlorous \ ^->
Alcohol. j^pjj Acetic ether.
Amylic alcohol, treated in like manner, yielded valerianate of
amyle.
By the action of an aqueous solution of chlorous acid on urea,
a body was obtained crystallizing in large flat prisms, which
were very hygroscopic. Its composition was found to be
C^ H^ N^ CI 0^. It might be regarded as a compound of urea and
sal-ammoniac, C^ H'* N^ 0- + N H'^ CI. By crystallizing together
equivalents of these substances, this body could not be obtained.
By the action of aqueous chlorous acid on uric acid, a new
acid was obtained crystallizing in pearly laminse, which formed
* Liebig's Annalen, October 1859.
Composition of the Gas in non-luminous Flames. 121-
ciystalline salts with baryta and lead, and with silver a caseous
precipitate. Its composition is C^^ H'* ^s" 0" ; and Schicl names
it chloraluric acid. Besides this, other bodies arc formed, the
investigation of which is not complete.
The gas in the dark cone of the non-luminous flame of Bun-
sen^s gas-burner is a mixture of atmospheric air and coal-gas.
Lunge* has analysed this gas with a view to ascertain the ])ropor-
tions in which these two constituents exist. To collect the gas,
the following method was adopted : — In the upper part of the
burner, a few millimetres below the mouth, a small aperture was
made through which a fine, bent glass tube was so introduced
that it stood exactly in the middle of the aperture of the burner,
and projected about 17 millims. above. The diameter of this
tube was about O'S millira.; it was fastened in the burner by
means of gypsum, and its other end was connected by means of
caoutchouc with two wide gas- collecting tubes. The caoutchouc
junctions could be closed by means of Mohr's stopcocks. The
last gas-tube was connected with an aspirator under a constant
pressure, the efflux of which could be regulated by a tap.
The flame was so regulated that its height was about 136 mil-
lims. ; the internal cone vras about Gl millims. high. The aspi-
rator was then set in motion, and a stream of gas withdrawn so
slowly that the dimensions of the flame were scarcely altered.
When the tubes were full they were closed, and transferred to a
eudiometer.
The analysis of the gas, made according to the methods de-
scribed in Bunscn's gasometric methods, gave the following
results for the composition of the mixture : —
Carbonic acid 0-00
Oxygen 14-28
Elayle 1'67
Dit'etryle 076
Carbonic oxide .... 2" 73
Hydrogen 11 "94
Marsh-gas 12-97
Nitrogen 55-65
] 00-00
Earlier analyses of the Heidelberg gas (which was used in this
investigation), as well as some analyses made simultaneously
with this research, showed that it contained no oxygen ; and
hence all the oxygen found could be assigned to the atmospheric
air of the mixture, the quantity of which was accordingly 68*13
* Liebig's Annalen, November 1859.
ij^- M. Louren90 on Glycol.
per cent. There remains, therefore, 31 "78 per cent, gas of the
following composition : —
Carbonic acid .... 0*00
Oxygen 000
Elayle 5-2i
Ditetryle ...... 2-38
Carbonic oxide .... 8'58
Hydrogen 37*46
Marsh-gas 40*70
Nitrogen 5-64
100-00
This composition agrees with other analyses of Heidelberg gas,
and from it may be calculated the quantity of oxygen (i. e. air)
necessary for the perfect combustion of the gas which must reach
it from the outside. For —
1-67 vol. Elayle requires . . 5-01 vol. oxygen.
0-76 „ Ditetryle „ . 4-56 „
2*73 „ Carbonic oxide . . 1"37 „
11-94 „ Hydrogen „ . . 5-97
12-97 „ Marsh-gas „ . . 25 94 „
42-85
From this it appears that 100 parts of this gas mixture still
require 42-85 — 14-28 = 28'57 parts of oxygen, which correspond
to 136-30 parts of air. Hence in the flame of this burner, almost
exactly one-third of the oxygen (i. e. air) necessary for complete
combustion reaches it from the interior.
Lunge has also calculated, according to the methods described
in Bunsen's work, the temperature of the flame for this gas. He
finds that it is 2781° C.
In the expectation of forming oxide of ethylene* directly from
glycol in accordance with the following equation, Louren9ot
heated together glycol and bromide of ethylene :
J3(^'2tloA-fG2H4Br2=2(^'2'\o)+2G2H^O + 2H20.
^ ru ^ Bromide of t> Oxide of
'^h-^o^' ethylene. ^^' . ethylene.
Hydro bromic
glycol.
Hydrobromic glycol and water were formed; but instead of
oxide of ethylene, a substance is obtained boiling above 230' C,
having a sweet taste, the consistence of glycerine, and perfectly
* Phil. Mag. vol. xvii. p. 427.
t Bulletin de la Soc. Chimique, p. 77.
+ G=12; 6=16; 0=6; 0=8.
M. Wurtz on Derivatives of Ghjcol. ISi
soluble in water, alcohol, and ether. Repeated analyses and a
vapour-density determination gave for it the formula G'^H'^O^,
and its formation may be thus expressed : —
3(^'JJJlo^')+^'H4Br2=3/^'^'^o\+€4HioO3 + H20.
V ^, J Bromide of \ i^ / New body.
CJly^^ol- ethylene. ^"^
Hydrobromic glycol.
In its composition it is intermediate betAveen glycol and the ether
of glycol ; it may be represented as two molecules of glycol united,
with the elimination of an atom of water :
\q2
Wurtz* has published some additional researches on oxide of
ethylene. Oxide of ethylene has the properties of a base ; it
combines directly with hydrochloric acid to form hydrochloric
glycol :
HCl + e^H^O = G2H4HC10= H J^*
Oxide of CI
ethylene. Hydrochloric glycol.
It also combines directly with acetic acid to form the acetate of
glycol.
It combines with water to regenerate glycol. The two sub-
stances are heated together in a sealed tube. The product of the
action has a saccharine taste. On distillation, glycol first passes
over, and the temperature rises to about 210°. The distillate
then consists of the intermediate ether of Louren90 above de-
scribed. Its formation and that of glycol are expressed by the
reactions :
G2H4O+H2O = G2H602.
Oxide of Glycol,
ethylene.
2(G2IIt0) +IF9=G'*H»0O3.
Oxide of Intermediate
ethylene. ether.
Wurtz points out that this intermediate ether bears to glycol and
oxide of ethylene the same relations as Pelouze's anhydrous lactic
acid does to l&ctic acid, and to lactide.
* Bulletin de la Soc. Chimique, \). 7^-
124
M. Wurtz on Derivatives of Ghjcol.
■03
O^
W J
PelouzL'^s anhydrous
lactic acid.
Lactic acid.
G2 H
11-2 J
Intermediate
ether.
G«H4"
Glycol.
G-2H4"0 G^H^O".©.
Oxide of ethylene. Lactide.
Oxide of ethylene also* unites with glycol under the same
circumstances as with water. The principal product of the reac-
tion is the above intermediate cthcr^ €'*I1"^<3^; but when this
has distilled over, a very thick colourless liquid is obtained which
boils at about 290''. It is formed by the combination of two
atoms of oxide of ethylene with one atom of glycol; and its com-
position is expressed by the formula
2{Q-^W^) + G2H6 02=G«Hi4 94^
Oxide of ethylene. Glycol. New body.
It is also formed, but in very small quantities, by the action of
oxide of ethylene on water :
3(G2H^O) + H2 0=G6H'4O4.
Oxide of ethylene. New body.
Hence one, two, or three atoms of oxide of ethylene can unite
with one atom of water to form, by direct synthesis, more and
more complicated bodies, which are nevertheless very simple in
their molecular constitution. Wurtz considers these bodies to be
alcohols. If the name ethylenic alcohol be given to glycol, the
other two bodies may be iiamed diethylenic alcohol and triethy-
lenic alcohol. The following formuke indicate the relations of
these bodies to each other : —
G^ H^"^ r>2 derivative of the
H^ J diatomic type
Ethylenic alcohol.
G^H^"
G2H«02='
Glycol.
Hn
HV
0^.
e4Hl<J 03 = ^2 11-*
M. Louren^o's H
compound.
•03
derivative of the
triatomic type
New bodv.
Diethylenic
alcohol.
G^H^" I ^4 derivative of the
g-2jj4' r tetratomic tvpe
hO
Triethyleuic alcohol.
* Comptes Rendus, November 21, IS59.
-O".
MAVmtz on Derivatives of GhjcoL 125
Wur'.z has also* found that oxide of ethylene can combme
directly with ammonia to form very powerful organic bases.
"When oxide of ethylene is added to a concentrated aqueous solu-
tion of ammonia, the two bodies combine with great energy ; and
on evaporating the mixture, a strongly alkaline liquor is obtained.
By neutralization with hydrochloric acid and further evaporation,
brilliant colourless rhombohedra are obtained which have the
formula
€«H'5NG^ HCl.
With bichloride of platinum this body combines to form a double
salt which crystallizes in golden yellow laminse ; the composition
of this body is expressed by the formula
G^HisNO^HCl, PtCF.
The mother-liquor from the above rhombohedra contains an
uncrystallizable hydrochloratc. When this is evaporated and
bichloride of platinum added, a double salt is obtained which
crystallizes in magnificent orange-red rhomboidal prisms; their
composition is
e4HiiN0^HCl,PtCP.
The base contained in the latter platinum-salt contains the ele-
ments of an atom of ammonia, and of two atoms of oxide of
ethylene j its formation is thus expressed :
Oxide of x- 1 ^
ethylene. ^^"' ^''^''^
The base contained in the rhombohcdric hydrochloratc con-
tains the elements of an atom of ammonia, and of three atoms of
oxide of ethylene. Thus :
3GMI40-hNIP=€2II40 ^NIP=G«ir5N03.
Oxide of e^H'^oJ
ethylene. New base.
These bases result from the tendency which oxide of ethylene
exhibits when added to the elements of another body to form
direct combinations, and also to double or triple its molecule.
Unlike the compound ammonias, these bases arc not formed by
substitution, but by direct addition ; they are ratlier to be
regarded as conjugated aunnonias, and seem to supj)ort the idea
of Berzelius, tliat the; alkaloids contain ammonia ready formed.
AVurtz considers, nevertheless, that they bolong to the ammonia
type, and reserves for a future connuunication the discussion of
their constitution.
* Coinptes RenJus, December 3, ''Si>\h
12^ Prof. Knoblaucli on the Interference vf Heat.
It is obvious, as "Wurtz remarks, tiiat by treating oxide of
ethylene with compound ammonias, a great variety of artificial
alkaloids containing oxygen may be obtained.
Bohn* has investigated the optical relations of the tartaric
aicid prepared artificially by Liebig, by the action of nitric acid
on sugar of milk. He finds that they are quite identical with
those of the ordinary tartaric acid.
XVI. On the Interference of Heat.
By Professor Knoblauch f.
THE diff'erences of phase observed by Prof. Knoblauch in
the setherial oscillations of interfering thermic rays were
produced in the following four difierent ways.
1. Difference of phase in consequence of unequal lengths of path
in one and the same medium.
A beam of solar light, after being reflected by a heliostat,
entered through a slit, from 4 to 6 millims, wide, into a dark
room, and at about 2'3 metres from the window fell upon a glass
gi-ate behind which was placed an achromatic glass lens. When
a square thermo-electric pile (whose anterior opening could be
narrowed or widened by means of wings) was placed at about
0*5 metre from the lens in different parts of the interference-
spectrum there formed, a multiplier connected with the thermo-
electric pile showed deflections varying, according to the fine-
ness of the grate, from 2°'15 to 18°'5 when the pile entered
the central white luminous field. The needle of the multiplier
returned to its zero-point when the thermoscope was placed in
one of the dark bands to the right or left of the centre. It
became deflected again, however, to 0''6 or 0^*7 as soon as the
instrument was moved into either of the next following coloured
spectra. AVith very fine grates, the increased cold between the
first and second spectra could be detected with certainty.
The phenomenon was clearest vaih. finely scratched plates of
rock-crystal, behind which the indications of the thermo-multi-
plier were the following : —
2° in the central white . . 2'5 millims. broad,
0° in the first dark band . . 90 millims. broad,
1°'25 in the first spectrum . 8-5 millims. broad,
0° in the second dark baud . 1'25 millims. broad,
0°'87 in the second spectrum . 15-0 millims. broad.
* Comptes Rendus, December 3, 1859.
t From the Monthly Reports of the Royal Academy of Sciences at Berlin.
Prof. Knoblauch on the Interference of Heat. 127
In order to diminish to the utmost the absorption in the tra-
versed media, and thus to increase the intensity of the effects,
a grate and lens of rock-salt were employed. With such a
grate, containing GOO lines in an inch, the deflection for the
centre was 31°'0, and for the first spectrum 1°*5 ; these two lumi-
nous bands were separated by a colder one corresponding to a
deflection of 0°*3. With a finer grate the deflection was observed
to be \7°'25 in the centre, 3"'5 in the first spectrum, and only
0°"5 between the two. The deflections which with rock-salt
remain on the dark bands are due to diffusion of the rays, which,
with this substance, cannot be avoided.
The above effects can certainly not be ascribed to accidental
secondary actions ; for the several differences of temperature
were still observable when the pile exposed the same surface
during its displacements, or even when it presented a greater
aperture to the rays in the dark bands.
At the same time a new proof of the divergence of the rays
of heat through inflexion may be deduced from these experi-
ments. For whilst, without the grate, the enclosing limits of
these rays at the place of measurement were, saj'^, 2*5 millims.
apart, after replacing the grate the extreme limits of heat were
not even reached at a distance of 300 millims. on each side of
the centre; consequently at places which were 600 millims*
distant from each other.
2. Diffei'ence of phase iviih the same length of path in consequence
of the passage of rays through a body of unequal thickness.
After interference-bands had been produced by introducing
into the path of the solar rays an interference-prism in place of
the grate, and a cylindrical glass lens in place of the achromatic
one or the rock-salt lens, and after the thermo-electric pile had in
this case, too, distinguished in the most unmistakeable manner
the dark bunds from the neighbouring light ones by a deflection
of from 0°-25 to 1^*25 at the multiplier, a somewhat conical
strip of glass was interposed behind the interference-prism, in
such a manner that the rays of heat, in order to traverse one-
half of the same, had to pass through a greater thickness of
glass than was necessary in order to traverse the other half. By
this means a displacement of the interference-bands was pro-
duced ; for the thermo-multiplier indicated a decrease of tempe-
rature, on the introduction of the glass, when the thermic pile
was at a place of original maximum of heat, and an increase of
temperature when the pile was situated in one of the former cold
bands : this latter fact is the more significant, since the action
was there opposed by the absorption of the interposed glass. With
respect to interference, therefore, the influence of unequal thick-
128 Prof. Knoblauch on the Interference of Heat.
nesses of traversed glass is such that places of greater heat
become colder, and vice versd.
3. Difference of phase through unequal rejlexion.
If, according to the principle of the representation of New-
ton's rings, solar rays are reflected from a flint-glass convex at
its lower surface, and from a plane glass under the former con-
sisting half of flint- and half of crown-glass ; if, further, between
the two a liquid be introduced which, like clove-oil, is inferior
to flint-glass, but superior to crown-glass in refracting power,
the rays will in the one case pass first from a greater to a less
refracting substance, and then from a less to a greater; whilst
in the other case these rays will pass twice, successively, from a
greater to a less refracting medium. The interfcrence-phseno-
mena, which in the first case consist of a series of rings with a
dark centre, and in the second of a series with a light centre,
being thrown on a screen by means of a lens, and the screen
being replaced by a thermo-electric pile, the temperature in the
one centre is found to be so low that the needle of the multiplier
is only deflected 0°*5, whilst in the other centre it is so high as
to cause a deflection of 3°. Laurel, aniseed, calamus, and cassia
oils deport themselves like clove-oil ; whilst with lavender, ber-
gamot, and citron oil, &c., as also with water and air, their in-
dices of refraction being even less than that of crown-glass, both
centres have a lower temperature.
When the double plate of flint- and crown-glass is replaced by
one of calcareous spar bounded by the ordinary surfaces of clea-
vage, two groups of interference-ph0enomena are also obtained
by employing the first-mentioned oils, since their indices of
refraction lie between those of the ordinary and extraordinary
rays in the calcareous spar; these phenomena can only be sepa-
rated, however, by interposing a Nicol's prism between the pile
and the interference-apparatus. In the one case, corresponding
to the dark centre, a deflection of 0°'25 was obtained; in the
other case, corresponding to the light centre, a deflection of 2°'5,
and these according as the principal section of the Nicol's prism
and that of the rhomb of calcareous s])ar were inclined at 90° or
were parallel to each other. By every position of the Nicol's
prism the centre of the rings had the same low temperature
when, between the convex flint-glass and the calcareous spar, one
of those substances were interposed whose index of refraction is
smaller than that of the extraordinary ray in the calcareous spar.
4. Difference of phase produced by unequal velocities of doubly-
refracted rays.
In order to obtain rectilinear bands by means of double refrac-
tion in the polarizing apparatus, it is best to use two plates of
Dr. Wright on the Behaviour of Mercury as an Electrode. 129
rock-crystal cut parallel to the natural pyramidal surfaces, to
place them one above the other in such a manner that their
principal sections form an angle of 90° with each other, and to
introduce them between the glass-piece and tourmaline, or be-
tween the glass-piece and Nicol. A lens then throws these
bands objectively upon a suspended screen or upon the thermo-
electric pile.
It appeared to promise interest to examine also in this field
the quality of the thermic colours produced by interference. In
order to obtain the latter, a thin plate of gypsum was introduced
between two NicoPs prisms, 85 millims. in length and 42 mil-
lims. in diameter. The test itself was instituted by means of
diathermanous substances, such as coloured glasses, placed suc-
cessively before the pile. Observation proved that equal quan-
tities of rays of heat, after passing through the polarizing appa-
ratus and the gypsum, possess in different degrees the power of
traversing the same diathermanous substance according as the
principal sections of the polarizing and analysing Nicols cross
each other at right angles or are parallel; further, that both
these groups of rays differ from that which corresponds to an
angle of 45° between the principal sections of the two Nicols,
and which constitutes the transition from any thermic colour to
its complementary one.
XVII. Remarks on the behaviour of Mercury as an Electrode.
By T. Stiiethill Wright, M.D., President of the Royal
Physical Society, Ediribmyh^.
THE voltaic movements of mercury have been investigated by
Davy, Gerbour, Hellwig, Erman, Pfaff, and Runge, and
especially by Sir John Herschcl, who almost exhausted the sub-
ject in the Bakerian Lecture for 1824. The great majority of my
observations were similar to those made by the authors above men-
tioned. I shall therefore not detail them to the Society tonight,
but merely bring forward those which a])pcar to be new.
Experiment 1 . — An ounce of mercury was poured into a shallow
vessel containing a quantity of sul])huric acid diluted with water,
sufficient to cover the surface of the metal. The mercury was
then connected by a line copper wire with one of the terminal
wires of a galvanometer. The other wire of the galvanometer
was armed with a small plate of amalgamated zinc ; the whole
consequently formed a voltaic circle of zinc, mercury, and dilute
acid. On plunging the zinc plate into the acid, the needle was
* Extracted fioni a paper coniraunicateil to the Royal Society of Eilin-
buri>h on the 21st of Febniarv, 185i>,
Phil. Mag. S. 4. Vol. 19. No. 125. Feb, 1860. K.
130 Dr. Wright on the Behaviour of Mercury as an Electrode.
deflected to 90°, and the mercury, which lay extended against the
side of the vessel, contracted itself into a more globular form,
and, throwing off the liquid from its surface, appeared above the
latter dry and bright. The instant, however, that the mercury
had become contracted, the needle of the galvanometer returned
to zero ; indicating the cessation of the powerful current which
had passed at the first completion of the circuit. The zinc plate
was then removed from the liquid, and the mercury, after
remaining contracted for a short time, rcassumed its elongated
form and hid itself beneath the acid.
Experiment 2. — The mercury was brought to the contracted
state as before, and the zinc plate quickly changed for one of
platinum. The fluid metal now quickly extended itself; and at
the same time a momentary current of great energy was indi-
cated by the galvanometer, but passing in a contrary direction
to that obtained by the former arrangement with zinc.
Experiment 3. — The galvanometer was removed, and the zinc
brought for an instant in contact with the mercury ; by which
means a slight addition of zinc to the mercury was effected.
The result was a contracted state of the mercury which continued
for eight hours. The globule so contracted was then connected
with a plate of platinum immersed in the solution, when an
evolution of hydrogen commenced on the surface of the platinum
which continued until the mercury suddenly resumed its ex-
tended shape.
These experiments appear to indicate that the first effect of
communication by a connecting wire between the mercury and
zinc, was to set in motion a current which deposited a thin layer
or film of hydrogen over the whole surface of the mercury. The
metal being thus released from its attraction for the acid,
assumed a form still more globular than it possessed in air, in
consequence of the support it received from the liquid surround-
ing it. The extension of the mercury, which occurred after the
interruption of the circuit, was probably in consequence of the
union of the film of hydrogen with the oxygen of the atmo-
spheric air contained in the water.
Exj)eriment 4. — A portion of mercury A, brought into the con-
tracted state as in Exp. 1, was connected, by means of a thin
wire, with a second portion of mercury B. B instantly con-
tracted itself as if A had been a plate of zinc.
Similar but less energetic contractions took place in mercury
immersed in solutions of common salt, iodide of potassium, and
other alkaline salts.
The rapidity of contraction and extension in the mercury was
greatly enhanced by the addition of a little nitric acid to the
sulphuric acid solution. Indeed, by placing the extremity of the
Dr. Wright on the Behaviour of Mercury as an Electrode. 131
connecting wire in such a position that the mercury when ex-
tending fell against it, a series of contractions and extensions
took place in such rapid succession that the eye had some diffi-
culty in following them.
Experiment 5. — Two portions of mercury were immersed in
dilute sulphuric acid ; A was brought into connexion with the
anode or positive pole of a Daniel's battery of six pairs, and B
with the cathode or negative pole of the same. A instantly
became covered with a silvery film of oxide, flattened itself out
into a thin plate, and slowly crept up to and around B, which
was contracted and covered by bubbles of hydrogen.
Experiment 6. — Dilute hydrochloric acid was substituted for
the sulphuric acid solution of the last experiment. A instantly
became covered with a dark brown coating of chloride, and in
this state could be drawn out into long threads or branches. The
direction of the current was now suddenly reversed, when A
drew in all its branches as by magic, and, after rotating violently,
assumed the contracted state.
Experiment 7. — A quantity of mercury was strained through
muslin into a solution of common salt in water, and lay in a
divided state at the bottom of the vessel. When .all was quiet,
the induced and interrupted cm-rent from the primary wire of a
powerful electro-magnetic coil machine was passed through the
solution. The globules of mercury instantly began to unite with
each other, and did not cease to do so until the whole formed a
single mass.
The above experiments seem to me to prove the propositions
of Erman : — 1 st. " That so soon as chemical affinities are excited
in the galvanic processes, there takes place at the same time an
increased intensity of the attraction of surfaces " (that is, of
capillary attraction). 2nd. " That the connexion which has been
supposed to exist between capillary or surface attraction and
chemical affinity, receives from this a notable confirmation."
It has been already stated that in solutions of chloride of
sodium, and other alkaline salts, contraction occurs in mercury
when rendered the negative element or cathode of a single circle.
When, however, in such solutions mercury is made one of the
negative elements of a compound circle of high tension, a stronger
chemical affinity is set up between the mercury and the liquid,
the metal of the alkaline solution is reduced and combines with
the mercury, and the latter yielding to an increase of capillary
attraction, instead of contracting, expands.
Experiment 8. — One ounce of mercury was placed in a saucer
containing a solution of chloride of sodium, and was connected
with the negative wire of a Grove's cell. The positive wire of the
same cell, armed with a piece of zinc, waa now dipped into the
K2
132 Dr. Wright on the Behaviour of Mercury as an Electrode.
solution. The mercury extended itself, and was driven with
violence in the direction of the zinc. At the same time the
strong currents were set up in the solution which have been so
fully described by llerschel and others.
Experiment 9. — A common dinner plate was inverted, and a nar-
row strip of silver cemented across its bottom. This strip served
to retain a large pool of nicrcuiy in the centre of the plate. A
solution of iodide of potassium was now poured on the plate, and
two iron wires dipping into the liquid transmitted the current of
twelve small DanieFs cells across the plate and the silver strip.
The mass of mercury immediately commenced flowing to and
fro between the wires, touching and receiving an impulse from
each wire alternately. By employing several pounds of mercury,
the last experiment might be rendered a very striking illustration
of the galvanoscopic properties of mercury before a large audience.
Undulatory Motions of Mercury.
Two globules of mercury immersed in a solution of chloride of
sodium were connected with the ends of the primary wire of an
electro-magnetic coil machine. AVhen the machine was slowly set
in motion, the mercury undulated in two directions so as to repre-
sent a cross. Increasing speed in the action of tlie break caused
the metal to assume successively the form of a star with six,
eight, twelve, or more rays. Occasionally, also, these stars
would revolve slowly on their centres.
A large pool of mercury under the same circumstances had
its entire surface throv,n into innumerable waves, which showed,
by their mutual interference, figures of remarkable complexity,
when examined by a reflected beam of light. These figures were
always constant for the same speed of break, power of battery,
and shape of the mercury.
Having noticed on several occasions the occurrence of un-
dulatory motions in mercury when traversed by a constant cur-
rent, I endeavoured to reproduce these motions, but for some
time in vain. At last I found that they took place in a solution
of chloride of sodium containing a very small quantity of sul-
phuric acid; in the former of which solutions mercury expands,
while in the latter it contracts. This beautiful experiment as
perfected was performed as follows : — A plate of zinc three inches
in diameter, having a wire soldered to it, is sewed up in muslin
and cemented in the centre of a white dinner plate. A quantity
of mercury is then poured into the plate until it lies as a fluid
ring round the bottom and at about two inches distant from the
zinc. The metals are now covered with a clear saturated solution
of chloride of sodium. The wire soldered to the central piece of
zinc is connected with the positive pole of a platinized zinc
Prof. LeContc on the Correlation of Forces. 133
battery* of two cells, while a wire connects the negative pole of
the battery with the mercury. The mercurial ring now flattens
itself out, and strong currents pass through the solution from the
zinc to the mercury. Very dilute sulphuric acid is now added
drop by drop, until all at once the currents in the solution stop,
and the whole of the inner edge of the mercury is thrown into
large waves of equal size which flow rapidly round the circle, the
mercury assuming the appearance of a ring with large rounded
teeth in rapid rotation. A further addition of acid increases the
rapidity of the undulations, and at the same time decreases the
size of the waves, until at last it stops them altogether, and the
mercury becomes contracted. The mass of the mercury has no
rotatory movement even when the undulations are the most ener-
getic. At first the waves often pass in opposite directions in
different parts of the ring, until the longer set compels the
shorter to change its course, and they all pass round in the
same direction.
XVIII. The Correlation of Physical, Chemical, and Vital Torce,
and the Conservation of Force in Vital Phcenomena. By Joseph
LeConte, Professor of Geology and Chemistry in the South
Carolina College, Columbia-f,
MATTER constantly changes its form, but is itself inde-
structible, except by the same power which called it
into being. The same quantity of matter exists in the uni-
verse at all times. So also force changes its form constantly,
but is itself indestructible, incapable of increase or diminution,
and the same absolute amount of force exists in the universe at
all times and for ever. The mutual convertibility of the various
forms of force is called " correlation of forces.^' The mvariability
of the absolute amount in the midst of constant change is called
" conservation of force." This principle of correlation and con-
servation of force must be looked upon as one of the grandest
generalizations in modern science, — a principle startling at first,
but when clearly understood and firmly grasped, almost axiom-
atic. It must be considered a necessary truth, and, as such, is
a legitimate basis of deductive reasoning.
The correlation of physical forces is universally recognized as
a principle in science, and not only so, but has already been pro-
* I have for some years used; tliis battery, in which the platinum and
nitric acid of Grove's battery are ,'changed for the thinnest sheet zinc
brushed overwitli a very dilute solution of chloride of jthitinum, and a
nitro-sulphuric acid consistinq; of five ]iarts by measure of sulphuric acid
to one of nitric acid. Zinc is not acted upon by this mixture.
t From Silliman's American Journal for November 1859.
134 Prof. LeConte 07i the Correlation of Forces.
ductivc of many beautiful and useful results ; but the correlation
of physical and vital forces, while generally recognized as a pro-
bable fact, has only been speculated on in a vague and as yet
unfruitful manner. The science of life is scarcely yet ripe for
the legitimate extension of this principle over its domain. The
most elaborate attempt of this kind which I have seen is con-
tained in the very remarkable and suggestive paper of Dr. Car-
penter, entitled " Mutual Relation of Physical and Vital Forces,"
and pubUshed in the Philosophical Transactions for the year 1850.
In the present paper I wish simply to present a few thoughts
which have originated in my own mind in the course of reflec-
tion on this subject, in the hope that they may prove suggestive
to others. They have at least the merit of being uninfluenced
by the writings of others, and therefore perhaps of presenting
the subject in a somewhat new light. I sincerely wish I could
present the matter in a more definite form ; but it is certain that,
where a subject is not perfectly understood, the attempt to give
our ideas more definiteness also makes them more questionable.
We are obliged to be content with a certain vagueness, in the
hope that by the use of right methods a clearness will come
after. We must gratefully accept the twilight in the hope that
it marks the approach of the full light of day.
There are four planes of material existence which may be re-
garded as being raised one above the other. The fist and lowest
is the plane of elementary existence; the second, the plane of
chemical compounds, or mineral kingdom ; thh-d, the plane of
vegetable existence; and fourth, of animal existence. Now it is
apparently impossible for any known force in nature to raise
matter through all these grades at once. On the contrary, there
is a special force adapted for the elevation of matter from each
plane to the plane above. It is the special function of chemical
affinity to raise matter from plane No. 1 to No. 2. All the
changes, too, which take place upon plane No. 2 by the mutual
reactions of bodies situated on that plane, are under the guidance
and control of this force. It is the special prerogative of the
force of vegetation — of vegetable life — to lift matter from No. 2
to No. 3, i. e. from the condition of mineral matter to the higher
condition of vegetable matter. All the changes which take place
upon this plane, the laws of which constitute vegetable physio-
logy, are under the guidance of this force. Finally, the force of
animal life, and that alone, enjoys the privilege of lifting mat-
ter still higher, into the fourth plane, i. e. the plane of animal
existence. No force in nature can lift from No. 1 to No. 3, or
from No. 2 to No. 4. Plants cannot feed entirely upon ele-
mentary matter, nor can animals feed upon mineral matter. The
reason of this will be seen in the sequel. Thus it seems that
Prof. LeConte on the Correlation of Forces. 135
after matter is raised from the elementary to the mineral con-
dition, it requires an additional force of another and peculiar
kind to raise it into the vegetable kingdom, and again another
accession of force to raise it into the animal kingdom. These
kingdoms arc therefore truly represented as successive planes
raised one above the other, thus :
No. 4. Animal kingdom.
3. Vegetable kingdom.
3. Mineral kingdom.
1. Elements.
If, then, it be admitted that this is the relative position of
these planes — that it requires a greater and greater expenditure
of force to maintain matter upou each successive plane, then it
follows that any amount of matter returning to a lower plane by
decomposition must set free or develope a force ivhich may, under
favourable circumstances, raise other matter from a lower to a higher
condition. Or to express it by a mechanical illustration, a given
amount of matter falling from one plane to any plane below,
developes a force sufficient to raise an equal quantity of matter
an equal height. Thus decomposition must in every case deve-
lope force, which force may take the form of heat as in combus-
tion, or electricity as in electrolysis, or may expend itself in
forming chemical compounds, or even in organizing matter.
Again, in the same manner as matter may be arranged in
several distinct and graduated kingdoms, so it seems to me the
forces of nature may also be properly divided into distinct
groups arranged in a similar manner one above the other. These
are the physical, the chemical, and the vital forces. iVjid as in
the case of matter, so also in the case of force, it is impossible to
pass directly from the lowest to the highest group without pass-
ing through the intermediate group. The conversion of physical
into vital force seems impossible without passing through the
intermediate condition of chemical force.
These are the simple principles upon which are based all that
follows, — principles which may possibly seem fanciful to some
unfamiliar with the principle of conservation of force ; but the
number of phsenomena which they consistently explain will, I
hope, entitle them to serious thought.
1st. It is well known that chemical elements, in what is called
the " nascent condition," i. e. at the moment of liberation from
previous combination, exhibit a peculiar energy of chemical
affinity not exhibited under other circumstances. It seems to
me that this is readily explicable on the principle of conserva-
tion of force. At the moment of decomposition the chemical
affinity which bound the elements together and which was be-
136 Prof. LeConte on the Correlation of Forces,
fore satisfied, is suddenly left unsatisfied. There is an attraction
set free which was before disguised — a force liberated which was
before latent. If conditions favourable are present, this force may
preserve the form of chemical affinity, and expend itself in form-
ing other chemical compounds, or even, as we shall see here-
after, in organizing matter. But if favourable conditions are not
present, then it may take some other form of force, e. g., heat or
electricity, and therefore no longer exist as chemical affinity: the
chemical affinity is said to be lost. To return to the mechanical
illustration used above. Matter falling from plane No. 2 to
plane No. 1, developes force sufficient to raise other matter from
plane No. 1 to No. 2, but which in the absence of such matter
may expend itself in heat or electricity, or some other form of
physical force.
2nd. It is a fact, now well established, that the seed in germi-
nation forms carbonic acid, and in doing so loses weight : that
is, the organized matter of the seed is partially decomposed, a
portion of its carbon uniting with the oxygen of the air to form
carbonic acid. Now it is this decomposition which developes the
force by which germination is eff'ected. A portion of the organic
matter of the seed is decomposed. This decomposition sets
free a force which suffices to organize the rest. The force neces-
sary, and therefore the amount of decomposition necessary in this
case is small, because the work to be accomplished is simply the
change from one form of organic matter to another, or rather
from organic to organized matter — to recur again to the former
illustration, merely shifting a certain quantity of matter from
one place to another upon the plane No. 3. " But how,^^ it may
be asked, "is this decomposition brought about ?^' This seems
to be efi^ected by the heat, and perhaps (according to Hunt) by
the actinic rays of the sun*. Heat and actinic rays have been
spoken of by many writers, e. g. by Carpenter and by Robert
Hunt, as the physical force which is changed into organizing
force by means of the " substratum of an organized structure :'^
but the peculiarity of the view which I now present is that this
conversion does not take place immediately, but only through the
mediation of another force more nearly allied to the vital, viz. che-
mical force. The food is laid up in the seed mostly in the form
of starch. In the act of germination this starch is changed into
sugar. Starch, as is well known, differs from sugar in two im-
portant respects, viz. it is insoluble, and it is more highly car-
bonizedf. Now, according to the ordinary view, the only object
* See Report by Robert Hunt on the Growth of Plants, Rep. Brit.
Assoc. 184G, p. 33 ; 1847, p. 30.
t Robert Hunt, Rep. Brit. Assoc. 1847, pp- 20-22. Carpenter, Comp.
Phys. p. 288. Mulder, Physiological Chemistry, pp. 208, 230.
Prof. LeContc on the Correlation of Forces. 137
of tlic partial decomposition is to change the food from an inso-
luhlc to a soluble form; and this can be done only by elimina-
tion of a portion of the carbon in the form of carbonic acid.
According to the view which I now present, the food is always
laid V J) in a more hicjhly carbonized condition than is wanted, in order
that force may he set free hy elimination of superfluous carbon. Ac-
cording to the ordinary view, if an insoluble food could be found
capable of conversion into the soluble form without loss of car-
bon, then germination of the seed might take place without
loss of weight, by the direct conversion of heat into vital force.
According to my view, decomposition, and therefore loss of weight
is absolutely necessary to develope the oryanizint/ force, the loss of
weight being in fact the exact measure of that force.
3rd. As soon as the plant dcvelopcs green leaves, a complete
change takes place in its mode of development. It no longer
loses weight, but increases in weight. It not only developes, but
grows. The reason of this is that the organizing force is no
longer developed by decomposition of food laid up within its
own tissues, but by the decomposition of food taken ab externo.
Sunlight is universally admitted to be the physical force con-
cerned in this decomposition. Further, it is generally supposed
that there is a direct and immediate conversion of light into
vital force in the green leaves of plants. But evidently this is
impossible, since i\\eicork done by the UcjJit is the separation of the
two elements carbon and oxygen. Light is therefore converted into
motion. It is therefore the chemical affinity thus set free which
is the force immediately converted into vital force. The food of
plants consists of carbonic acid, water, and ammonia (CO-, HO
and NIP), or in some cases, according to M. Ville, of CO^, HO
and N*. Sunlight acting through the medium of the green
leaves of plants has the remarkable poMcr of decomposing CO^,
The force thus set free from a latent condition, or the chemical
affinity of carbon in a nascent condition, is the foi^e by means of
which C, H, 0 and N are raised to the organic condition f. To
return to my former illustration : matter (oxygen) falling from
the second to the first plane developes force sufficient to raise
other matter from the second to the third plane. Thus it is
evidently impossible, on the principle of conservation of force, that
* See review of the controversy between Boussingault and Ville on this
subject, Bibl. Univ., Arch, des Sci. vol. xxx. p. 305. Also Phil. iMag. S. 4.
vol. xiii. p. 497. Ann. des Sci. S. 4. vol.ii. p. 35/. Anier. Journ. Science,
vol. xix. p. 409. Bibl. Univ., Arch, des Sci. vol. xxviii. p. 335. Anri. des
Sci. S. 4. vol. vii. p. 5.
t Ammonia is also probably decomposed in the tissues of the leaves of
plants (Carpenter, " Correlation ot" Physical and Vital Forces," Phil. Trans.
1850, p. 732. See also Morren, Bibl. Univ., Arch, des Sci., New Scries,
vol. v. p. 84). This would of course produce additional organizing force.
138 Prof. LeConte on the Correlation of Forces.
plants should feed entirely upon elementary matter ; whereas ac-
cording to the ordinary view of the direct conversion of light
into organizing force^ there is no reason why plants should not
feed entirely on elements, except that one of them, carbon, is
insoluble.
4th. There are many other phsenomena of vegetable life which
receive a ready explanation on this theory. I have said that
sunlight has the power of decomposing carbonic acid only in the
green leaves of plants. Pale plants, such as the Fungi among
cryptogams and the Monotropa among phsenogams, have no
power to decompose CO^. These plants, therefore, cannot feed
upon chemical compounds — mineral matter. They must feed upon
organic matter, which organic matter in its partial decomposition
furnishes the force necessary for organization. If so, then this de-
composition, as in the case of germination, must be attended
with the elimination of CO^. Both of these are known to be
facts. Pale plants do feed upon organic matter and do evolve
CO^. The necessary connexion of these facts with one another
and with the principle of conservation of force, is now for the
first time, as far as I know, brought out. The phsenomena of
nutrition in these plants is similar to that of seeds in germina-
tion, except that the latter contain the organic matter already
laid up within their own tissues, while the former derive it from
decaying vegetable or animal matter taken ab externo into their
tissues. In this case, too, as in germination, heat is apparently
the physical force which effects the decomposition of the organic
food, and which is therefore converted indirectly through chemi-
cal into vital force. Light is actually unfavourable to this process ;
for light tends to decompose, not to form CO^. In both cases
therefore the conditions favourable for nutrition are, first, abund-
ance of soluble organic matter, second, absence of light and
presence of heat. This is, then, apparently the true reason why
germinating plants and pale plants avoid the light. These plants
grow by the oxidation of carbon and formation of CO^. Light
decomposes CO^, and must therefore be antagonistic to its forma-
tion, and consequently to the growth of these plants. Whether
or not this property of light is entirely limited by the condition
of its acting through an organic tissue, is a question yet unde-
termined. Heat we know is favourable to the oxidation of car-
bon (combustion, fermentation, pvitrefaction, &c.) under all cir-
cumstances. Has light an opposite property also under all
circumstances ? or is this opposite property of light limited to
the condition of its acting through the medium of an organism ?
I hope the experiments already commenced, and still in progress,
by my brother Prof. John LeConte, and published in the last
' Proceedings * and in the American Journal of Science and Arts,
Prof. LeConte on the Correlation of Forces. 139
vol. xxiv. p. 317, will eventually furnish the means of solving
this very important problem. I do not wish to anticipate the
final results of these experiments; but it seems to me that the
negative resultrs thus far obtained rather support the view that
the action of light is not thus limited. In all experiments on
this subject the light and heat of the sun have been combined.
Now heat we know is favourable to combustion. The fact, then,
that combined light and heat produced no effect, would seem to
indicate that light counteracted the effect of the heat of the sun.
5th. Etiolated plants, or plants artificially blanched by exclu-
sion of light, exhibit the same phrenomena, and for the same
reason. These plants cannot receive their organizing force
through the decomposition of CO'^ by sunlight, therefore they
are obliged to obtain it from decomposition of organic matter.
Hence these plants require organic food ; hence also they evolve
CO^ instead of oxygen. In this case also decomposition of
organic matter, with a separation of a portion of the carbon in
the form of CO^, furnishes the organizing force. In the absence
of any external organic matter in the form of humus or manure,
etiolated plants, like germinating seeds, will feed for awhile upon
organic matter previously accumulated in their tissues in the
form of starch, and actually lose weight of solid matter*.
6th. In a most interesting and suggestive article in the Biblio-
theque Universelle {Archives ties Sciences-f) on the subject of
humus, M. Risler shows in the most conclusive manner that
organic matter in a soluble condition (soluble humus) is taken
up by almost all plants. This fact had been previously proved
experimentally by Th. de Saussure; but having been denied by
Liebig, it has been very generally neglected by vegetable physio-
logists. The doctrine of Liebig and of physiologists generally
is that, except in case of pale plants, organic matter is decom-
posed into CO^ HO, and NH^, i. e. must fall into the mineral
kingdom before it can be absorbed and assimilated by plants,
and therefore that organic manures only supply the same sub-
stances, and in exactly the same form, which are already sup-
plied, but in insufficient quantities, by the atmosphere. But
M. Kisler repeats with great care the experiments of De Saussure,
and confirms the accuracy of his conclusions. Hyacinths and
other bulbs were placed with their roots suspended in water co-
loured with soluble extract of humus. "When these plants were
placed in the sun, the water became rapidly decolorized. Other
roots, such as carrots, also germinating grains of wheat, were ob-
served to produce the same effects. An extract of humus was
exposed at a somewhat elevated temperature to sunlight under a
* Carpenter, Corap. Phys. j). 285.
t Bibl. Univ., Arch, des Sci., New Scries, vol. i. p. 305.
140 Prof. LeConte on the Correlation of Forces.
bell-glass. Microscopic plants developed in great abundance.
As long as these plants continued to develope, the infusion was
transparent and did not putrefy in the slightest degree; and yet
there was a constant evolution of CO^, as shown by analysis of
the air in the bell-glass. " Now the cellules formed in the liquid
contained carbon. This carbon did not come from the CO^ of
the air, for the liquid, far from absorbing, disengaged CO^. There-
fore the soluble humus must have furnished the carbon directly
to the vegetable cells.^^ It could not have furnished it indirectly
in the form of CO^ derived from decomposition of the organic
matter, otherwise oxygen, instead of CO'"^, would have been elimi-
nated. M. Risler thinks moreover that the embryo in germina-
tion takes up soluble organic matter in the form of humus in
addition to the soluble organic matter contained within the coty-
ledons, and that the evolution of CO^ by germinating seeds is
due in part also to the oxidation of humus. Finally, according
to the same author, the formation of roots in all plants, but par-
ticularly those containing much starch or sugar, is due to the
direct absorption of humus, and not, as is generally supposed,
to the fixation of carbon by means of light. " In order,^' says
he, " that CO^ of the air should form these substances, it is neces-
sary, in the beet and the potato, that there should be a descend-
ing sap, which there is not." Moreover, if the carbon were taken
from the soil in the form of CO^, there should be elimination of
oxygen instead of evolution of CO^ ; but the converse is the fact,
as has been proved in the most indisputable manner by De Saus-
sure and Boussingault*.
Mulder is equally explicit in affirming that plants absorb
soluble organic matter, which is converted in the roots, by elimi-
nation of a portion of the carbon, into starch and sugar (Mulder,
pp. 620, 664, 682). Thus, according to these authors, sap is
actually elaborated by the roots from organic manures.
Now according to the theory which 1 propose, this change
from humus into starch, sugar, or cellulose, furnishes an addi-
tional life-force. Humus is a more highly carbonized substance
than either starch or cellulose. By the partial decomposition of
humus in the tissues of the plant, with the elimination of a por-
tion of its carbon (removed by oxidation), a chemical force is set
free which serves to assimilate the remainder. Hence this pro-
cess of evolution of CO^, as we have already said, is opposed by-
light, but favoured by darkness and heat. Light favours the
formation of chlorophyll, of woody fibre, of essential oils, gums,
&c. ; darkness, heat, and organic manures favour the formation
of sugar, starch, &c. Hence the explanation of the well-known
fact, that by covering up the lower portions of potato plants by
* Bibl. Univ., Arch, des Sci., New Series, vol. i. p. 5.
Prof. LeConte on the Correlation of Forces. 141
heaping earth around them, many buds which would otherwise
form leafy branches develope into tubers. Hence also the expla-
nation of the equally well-known fact, that the roots of plants
seek and grow most rapidly in the direction of most abundant
food. If the sap is elaborated entirely in the leaves, it is diffi-
cult to understand why the descending sap should flow in greater
abundance in one direction than another. But if sap is elabo-
rated in the root itself, it is easy to see why growth is most rapid
in the direction of most abundant manure. It is easy to see,
too, why roots avoid the light ; since light decomposes CO^, and
therefore must be unfavourable to the formation of this substance.
7th. It is a well-known fact that the so-called respiration of
plants consists of two distinct and apparently opposite processes :
1st, the absorption of CO'- by the leaves, and also in solution by
the roots, the decomposition of this CO^ by means of light,
with the fixation of the carbon and the elimination of the oxy-
gen ; 2nd, the recomposition and evolution of CO^. The decom-
position of CO^ undoubtedly takes place in the leaves ; but where
the recomposition of CO'^ takes place is not so well ascertained.
It is exhaled, however, like the oxygen, from the leaves. The
process of decomposition of CO" takes place only during the day,
as light is absolutely necessary for this process. The recomposi-
tion of CO^ takes place night and day, although its exhalation,
according to some observers, seems to be more abundant during
the night. The process of decomposition of CO^ is well under-
stood ; of that of recomposition our knowledge is very imperfect.
M. Risler's explanation of this latter process seems most probable.
Plants, we have seen, undoubtedly absorb soluble organic mat-
ter, i. e. humus. Humus we know is a more highly carbonized
substance than cellulose or starch. This humus is therefore
oxidized in the roots and interior of the trunk, away from light,
by means of oxygen, also absorbed by the roots, and thus forms
CO'-^. This CO^ then circulates in the sap to be exhaled by the
leaves, or perhaps to be again decomposed by sunlight in these
organs. In the absence of light the whole is exhaled undecom-
posed. This readily accounts for the apparently greater exhala-
tion of CO^ during the night. A series of well-conducted ex-
periments would test the truth of this view. If it is true, there
should be a relation between the richness of the soil in organic
manures and the amount of CO^ exhaled. For a given amount
of growth, the amount of CO'^ exhaled is the measure of the
amount of food taken u]) in the form of organic matter, and the
amount of oxygen exhaled is the measure of the amount of food
taken in the form of mineral matter. Or if the exhaled CO- is
decomposed in the leaves during the day, then of course the
diflference between the amount exhaled during the night and day
142 Prof. LeConte on the Correlation of Forces.
would enter as an element in the calculation. Also, it would
seem that those plants especially which frequent rich shady
spots, should exhale proportionally more CO^ and less oxygen,
than those loving thin soils and sunny places.
In plants, then, there are two sources of organizing force, the
relative proportion of which varies infinitely, according to the
amount of light, heat, colour of the plant and richness of the soil
in organic matters. The two sources are immediately, 1st, the
decomposition of CO^, 2nd, the decomposition of soluble highly
carbonized organic matter ; remotely, the two sources are light
and heat. In plants which first take possession of desert spots,
bare rocks, &c., the first is the only source. In pale plants and
fungi the second is the only source ; but in most plants the two
are combined in various proportions. The first must of course
be considered the most fundamental and necessary, the second
being evidently supplementary. The decomposition of CO^ by
sunlight may be considered as the original source of all vegeta-
tion; but in most of the higher orders of plants the process of
nutrition is expedited by the reabsorption of organic matter
before it again returns to the condition of CO^, HO, and NH^.
8th. The e^^ during incubation absorbs oxygen, evolves CO^,
and probably HO, and loses weight. As the result of this evo-
lution of CO^, we find the egg developes. What it loses in weight
it gains in organization. Now what is the source of the organi-
zing force ? It evidently bears a direct relation to the loss of
weight. Here also, then, we have partial decomposition furnish-
ing the necessary force. A portion of the organic matter, falling
from the organic to the mineral plane, sets free a force which
raises the remaining portion into a slightly higher condition.
Heat is evidently the physical force or agent which is trans-
formed, not directly but indirectly, through chemical affinity into
vital force ; in other words, heat is the agent which effects the
necessary decomposition. The phfenomenon of development of
the egg is therefore very similar to that of the seed.
9th. After the hatching of the egg, the animal no longer loses
weight, because recomposition of food taken ab externo proceeds
jmri passu with decomposition. But in this case also decompo-
sition supplies the force by which recomposition is effected, and
growth and development carried on. As this is an important
point, I will attempt to explain it more fully.
It is well known that in the animal body there arc, going on
constantly, two distinct and a])parently opposite processes, viz.
decomposition and recomposition of the tissues; and that the
energy of the life is exactly in proportion to the rapidity of these
processes. Now according to the ordinary view, the animal body
must be looked upon as the scene of continual strife between
Prof. LeConte on the Correlation of Forces. 143
antagonistic forces, chemical and vital; the former constantly
tearing down and destroying, the latter as constantly building
up and repairing the breach. In this unnatural warfare the che-
mical forces are constantly victorious, so that the vital forces are
driven to the necessity of contenting themselves with the simple
work of reparation. As cell after cell is destroyed by chemical
forces, others are put in their place by \dtal forces, until finally
the vital forces give up the unequal contest, and death is the
result. I do not know if this view is held by the best scientific
minds at the present day as a fact, but it certainly is generally
regarded as the most convenient method of representing all the
pheenomena of animal life, and, as such, has passed into the best
literature of the age. Certain it is, however, that the usual
belief, even among the best physiologists, is that the animal
tissue is in a state of unstable equilibrium ; that constant de-
composition is the result of this instability ; and that this decom-
position, and this alone, creates the necessity of recomposition —
in other words, creates the necessity of food. But, according to
the view which I now propose, decomposition is necessary to de-
velope the force by which organization of food or nutrition is
effected, and by which the various purely animal functions of the
body are carried on : that decomposition not only creates the
necessity, but at the same time furnishes the force of recom-
position.
But it will no doubt be objected that, according to the princi-
ple of conservation of force, decomposition of a given amount
of matter can only effect the recomposition of an equal amoimt —
that a given quantity of matter falling a given height, can only
raise an equal quantity an equal height : the whole force deve-
loped by decomposition^seems to be expended in maintaining the
body at a given position. How then can growth and animal
activity go on? The answer to this question is obvious enough
when we recollect the nature of the food of animals. Animals,
it is well known, cannot feed upon mineral matter, but only on
food already organized, at least up to the vegetable condition.
But when decomposition takes place, the animal matter returns
no longer to the vegetable condition from which it was immedi-
ately raised, but to the mineral condition. It is decomposed into
CO''^ HO and urea. This last substance, though not strictly a
mineral substance, is far below the condition of vegetable matter.
Thus it is evident that a given quantity of matter falling down
from the condition of animal to that of mineral matter, i. e. from
the 4th to the 2nd plane, would develope force sufficient to lift a
larger quantity of matter from the vegetable to the animal condi-
tion, i. e. from the 3rd to the 4th plane, and yet perhaps leave
much residual force unexpended. Thus it is possible, and not
144 Prof. LeConte on the Correlation of Forces.
only possible but certain, on the principle of conservation of
force, that decomposition of animal tissues should set free a
force, a part of which is consumed in the recomposition of a
larger amount of new matter and thus maintaining growth, a
part in animal heat, and a part in animal activity of all sorts.
In this view of the case, we see at once the absolute necessity
that the food of animals should be organized. Upon the prin-
ciple of conservation of force, growth and animal activity — in a
word, animal life — would othcr\\'ise be impossible.
It follows also from the above, that the higher the organiza-
tion of the food, the smaller the amount of force necessary to
effect assimilation, and therefore the larger the amount of resi-
dual force to be expended in animal heat and animal activity.
In this we tind a ready explanation of the superior activity of
carnivorous animals, and the loss of animal activity which results
in a state of domestication from the use of vegetable diet ; also
of the supposed superior activity of men fed upon meat diet.
10th. I have spoken thus far of only one source of vital
force in animals, viz. the decomposition of the tissues. I have
attempted to show how, upon^ the principle of conservation
of force, this is sufficient to caiTy on the gi'owth and the activity
of the animal organism. But decomposition of the tissues,
though the fundamental source — the source characteristic of, and
peculiar to animals — of immediate and universal necessity in this
kingdom, and in many cases sufficient of itself, is not the only
source. There is also in animals, as in plants, a supplemental
source, viz. the decomposition of food.
It is well known that the food of animals consists of two kinds,
the nitrogenous, such as albumen, fibrine, caseine, &c. ; and the
non-nitrogenous, such as fat, starch, sugar, gum, &:c. According
to all physiologists since Liebig, the nitrogenous alone are used
in the repair and growth of the tissues. The non-nitrogenous
are either quickly consumed in resjnration, or else are laid up in
the form of fat for future consumption in the same way. Now
there can be no doubt that animals may live entirely on nitro-
genous food; in which case the whole vital force, whether for
assimilation of food or for animal heat and animal activity, is
derived from the decomposition of the tissues. This is the case
also, apparently, in the starving animal, particularly if lean. But
in almost all cases much food in the form of fat, starch, sugar,
&c. (non-nitrogenous),^ is never transformed at all into tissues,
but is taken into the blood, gradually decomposed, oxidized in
the course of the circulation, changed into CO" and HO, and
finally removed by exhalation from the lungs. Now what is
the object of the non-nitrogenous food, since these do not form
any part of the tissues, but are again decomposed and thrown
Prof. LeCoiite on the Correlation of Forces. 145
out of the system ? The answer usually given is that such food
is used in the animal economy solely as fuel to keep up the ani-
mal heat. On this view it is difficult to see why this class of
food should be used at all, especially in warm climates. But ac-
cording to the view which I propose we have here an additional
source of vital force. The decomposition of these ternary com-
pounds sets free a force which is used in organizing and assimi-
lating other matter (nitrogenous) and in producing animal acti-
vity and animal heat. As in plants, although the decomposition
of CO'^ by sunlight is all that is absolutely necessary for growth
and development, yet the decomposition of organic food sup-
plies an additional force which greatly increases the vigour and
rapidity of vegetation ; so in animals, although decomposition
of the tissues is all that is absolutely necessary to furnish the
force of growth and the phaenomena of animal life generally, yet
the decomposition of non-nitrogenous organic food furnishes ad-
ditional force by which growth and animal activity may be
maintained without too great an expenditure of the tissues.
11th. In what then consists the essential difterence between
animals and plants ? There can be no doubt that it consists,
generally, in their relations to one another and to the mineral
kingdom. Plants occupy a middle ground between the mineral
and animal kingdom — a necessary halting-place for matter in its
upward struggles. But when we attempt to define this relation
more accurately, the problem becomes much more difficult. It
is indeed probable that no single distinction will be found free
from objection. The commonly received and, to a certain ex-
tent, very correct idea, is that the essential distinction consists
in their relation to CO^. Plants decompose, and animals recom-
pose CO"^. The beautiful manner in which the two kingdoms
stand related to each other through these converse processes is
familiar to all. But it is well known that most plants carry on
both of these processes at the same time ; while some, as fungi,
pale ])lants, &c., only recompose CO', like animals. It seems to
me that at least an equally good fundamental distinction may
be found in this : that in plants the fundamental and necessary
source of vital force is the decomposition of its mineral food ;
while in animals the fundamental source of vital force is the de-
composition of its tissues. It is true that in what I have called
the supplementary source of vital force they seem to meet on
common ground, viz. the decomposition of organic food ; but
even here there is this essential difterence, that ni plants this de-
composition of organic food is only partial, and therefore fur-
nishes not only force but material for organization ; while in
animals the decomposition is complete and therefore furnishes
only force.
As a necessary result of the above, it would seem that the
Phil, Mag. S. 4. Vol. 19. No. 125. Feb, i860. L
146 Prof. LeConte on the Correlation of Forces.
" vortex " of Cuvier is characteristic of animals. There seems no
reason to believe that a tissue once formed in plants is ever de-
composed and regenerated, as is the case in animals. When
plant-cells decompose, the tissue dies. Hence the absolute ne-
cessity of continuous growth in plants. In this kingdom, life is
synonymous with growth. There is no possibility of life without
growth. There is no such thing as determinate size, shape, or
duration. There is no such thing as maturity ; or if so, death
takes place at the same instant. As cell-life is necessarily of
short duration, and as there is no regeneration of tissues in
plants, it is evident that the life of the tissues must be equally
short. Thus plant-life can only be maintained by the continual
formation of new tissues and a constant travelling of the vital
force from the old to the new. In exogenous plants the direc-
tion of travel is from the interior to the exterior; in endogeus
from exterior to interior, and still more from below upwards, by
the continual addition of new matter at the apex. In fungi, where
there is no such superposition of new tissue upon the old, where
growth takes place by multiplication of cells throughout the
whole plant — in other words, a true interstitial growth as in
animals — since there is no regeneration of tissues, the duration
of the life of the plant is limited by the duration of cell-life.
The respiration of animals, also, differs essentially from that of
plants. At one time the absorption of CO^ and exhalation of
0 was called the respiration of plants. It is universally admit-
ted now, however, that this is rather a process of assimilation
than of respiration. The recomposition and exhalation of CO^,
as soon as discovered, w^as very naturally likened to animal re-
spiration, and is in fact looked upon by many, as for example
the physiologist Carpenter, as a true respiration. But there is
an essential difference between this and animal respiration, which
1 have already pointed out. Its veiy significance is radically
different. The essential object of animal respiration is the re-
moval of poisonous decomposed matters from the organism.
The so-called respiration of plants, on the contrary, is rather a
process of assimilation, since by it the too highly carbonized or-
ganic food, by the elimination of a portion of its carbon, is
brought into a proper condition for organization, A true respi-
ration is necessarily connected with a change of the matter of
the tissues — v.ith the vortex of Cuvier — which has never been
shown to exist in plants. It is true the exlialation of CO* has
been looked upon by some physiologists as indicative of a re-
generation of tissues ; but I have already shown that this is
probably not the case, but, on the contrary, that the CO- is
formed by the partial decomposition of highly carbonized or-
ganic food.
1 2th. The most natural condition of matter is evidently that of
Prof. LeConte on the Correlation of Forces. 147
chemical compounds, i. e. the mineral kingdom. Matter separ-
ated from force would exist, of course, only as elementary matter
or on the first plane ; but united with force, it is thereby raised into
the second plane and continues to exist most naturally there.
The third plane is supplied from the second, and the fourth from
the third. Thus it is evident that the quantity of matter is great-
est on the second and least on the fourth plane. Thus nature
may be likened to a pyramid, of which the mineral kingdom
forms the base and the animal kingdom the apex. The absolute
necessity of this arrangement on the principle of the conserva-
tion of force may be thus expressed, flatter, force, and energy
are related to one another in physical and organic science sonie-
wdiat in the same manner as matter, velocity, and momentum in
mechanics. The whole energy remaining constant, the greater
the intensity of the force (the elevation in the scale of existence)
the less the quantity of matter. Thus necessarily results what
I have called the pyramid of nature, upon which organic forces
work upwards and physical and chemical forces downwards.
13th. As the matter of organisms is not created by them, but
is only so much matter withdrawn, borrowed as it were, from
the common fund of matter, to be restored at death ; so also
organic forces cannot be created by organisms, but must be re-
garded as so much force abstracted from the common fund of
force, to be again restored, the whole of it, at death*. If then
vital force is only transformed physical foi'ce, is it not possible,
it will be asked, that physical forces may generate organisms de
novo ? Do not the views presented above support the doctrines
of " equivocal generation '' and of the original creation of species
by physical forces ? I answer that the question of the origina-
tion of species is left exactly where it was found and where it
must always remain, viz. utterly beyond the limits of human
science. But although we can nev'cr hope by the light of science
to know how organisms originated, still all that we do know of
the laws of the organic and inorganic world seem to negative
the idea that physical or chemical forces acting upon inorganic
matter can produce them. Vital force is transformed physical
force : true, but the necessary medium of this transformation is
an organized fabric ; the necessary condition of the existence of
vital force is therefore the previous existence of an organism.
As the existence of })hysical forces cannot even be conceived
without the previous existence of matter as its necessary sub-
stratum, so the existence of vital force is inconceivable without
the previous existence of an organized structure as its necessary
substratum. In the words of Dr. Carpenter, " It is the speciality
of the material substratum thus furnishing the medium or in-
strument of the metamorphosis which estabhshes and must ever
* Carpenter, Phil. Trans. 1S50, ]). "ibb.
L2
1 i8 Royal Society : —
maintain a well-marked boundary line between physical and
vital forces. Starting with the abstract notion of force as ema-
nating at once from the Divine will, we might say that this
fprce operating through inorganic matter, manifests itself as
electricity, magnetism, light, heat, chemical affinity and mecha-
nical motion ; but that when directed through organized struc-
tures, it effects the operations of growth, development, and che-
mico-vital transformations."
XIX. Notices respecting New Books.
Elementary Geometrical Drawing. By S. H. Winter.
London : Longman, Green, Longman and Roberts. 1859.
THIS little handbook belongs to a class a great demand for which
has been created by the recently adopted system of competi-
tive examinations in connexion with our civil and military services.
These examinations, intended originally as tests, have very naturally
become objects of education, and, as such, liable to great abuse. In
general the demand of which we speak simply expresses a desire to
pass these examinations with the least possible amount of trouble,
and not unfrequently it indicates a tendency to evade the true spirit
of the test. Many of the books written to satisfy this demand, pro-
fessing to help the candidate through his examination rather than to
impart to him a thorough knowledge of his subject, are at once inac-
curate and superficial — in short, purely injurious. On this account,
rather than lor the merits of the best of them, they require to be
watched and carefully sifted. Convinced of the pernicious etfects of
such books, we felt compelled, not long ago, to condemn severely a
certain treatise on Practical Geometry ; today we are glad to be able
to speak more favourably of a more modest, and at the same time
more genuine work on the same subject. It is evident that Mr. Winter
could, if required, write a book of a much higher order, and on this
account he has been able to accomplish his simpler task creditably.
Few of his readers will fail to learn from him how to construct the
more essential geometrical figures ; and the more intelligent amongst
them, instead of finding their reasoning faculties unexercised, or
perhaps unrecognized, are continually invited to seek for a reason
for the construction they are taught to make. This is as it ought
to be ; and we trust that Mr. Winter's little book will meet with the
success it deserves.
XX. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Contimied from p. 75-]
May 26, 1859, — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.
THE following communication was read : —
" Remarks on Colour-Blindness." By Sir John F. W. Her-
schel, Bart., F,R,S.
[Extracted from a Report by Sk J. F. W. Herschel ou Mr. Pole's
Sir J. F. W. Hcrschcl on Colour-Blindness. 149
paper on the same subject*, and communicated at the request of the
President and Council.]
I consider tliis paper as in many respects an exceedingly valuable
contribution to our knowledge of the curious subject of colour-blind-
ness— 1st, because it is the only clear and consecutive account of
that affection which has yet been given by a party affected, in pos-
session of a knowledge of what has yet been said and written on it
by others, and of the theories advanced to account for it, and who,
from general education and habits of mind, is in a position to discuss
his own case scientifically ; and 2ndly, for the reasons the author
himself alleges why such a person is really more favourably situated
for describing the phenomena of colour-blindness, than any normal-
eyed person can possibly be. It is obvious that on the very same
principle that the latter considers himself entitled to refer all his per-
ceptions of colour to three primary or elementary sensations —
whether these three be red, blue, and yellow, as Mayer (followed in
this respect by the generality of those who have written on colours)
has done, or red, green, and violet, as suggested by Dr. Young,
reasoning on Wollaston's account of the appearance of the spectrum
to his eyes — on the very same principle is a person in Mr. Pole's
condition, or one of any other description of abnormal colour-vision,
quite equally entitled to be heard, w'hen he declares that he refers his
sensations of colour to two primary elements, whose combination in
various proportions he recognizes, or tliinks he recognizes, in all hues
presented to him, and which, if he pleases to call yellow and blue, no
one can gainsay him ; though, whether these terms express to him
the same sensations they suggest to us, or whether his sensation of
light with absence of colour corresponds to our white, is a question
■which must for ever remain open (although I think it probable that
such is really the case). All we are entitled to require on receiving
such testimony is, that the party giving it should have undergone
that sort of education of the sight and judgment, especially with
reference to the prismatic decomposition of natural and artificial
colours, for want of which the generality of persons whose vision is
tmimpeachably normal, appear to entertain very confused notions,
and are quite incapable of discussing the subject of colour in a
manner satisfactory to the photologist.
It is as necessary to distinguish between our sensations of colour,
and the qualities of the light producing them, as it is to distinguish
between bitterness, sweetness, sourness, saltness, &"C., and the che-
mical constitution of the several bodies which we call bitter, sweet,
&c. Whatever their views of prismatic analysis or composition
might suggest to Wollaston and Young, I cannot persuade myself
that either of them recognized the sensation of greenness as a con-
stituent of the sensations they received in viewing chrome yellow, or
the petal of a Marigold on the one hand, and ultramarine, or the
blue Salvia on the other ; or that they could fail to recognize a certain
redness in the colour of the violet, which Newton appears to have
had in view when he regarded the spectrum as a sort of octave of
colour, tracing in the repetition of redness in the extreme refrangible
* Phil. Mag. vol. xiii. p. 282.
150 Royal Society : —
ray, the commencement of a higher octave too feehle to affect the
sight in its superior tones. Speaking of my own sensations, I
should say that in fresh grass, or the laurel-leaf, I do not recognize
the sensation either of blue or of yellow, but something sui generis ;
■while, on the other hand, I never fail to be sensible of the presence
of the red element in either violet, or any of the hues to which the
name of purple is indiscriminately given ; and my impression in this
respect is borne out by the similar testimony of persons, good judges
of colour, whom I have questioned on the subject.
I would wish, then, to be understood as bearing in mind this
distinction when speaking of the composition of colours by the super-
position of coloured lights on the retina. It seems impossible to
reason on the joint or compound sensation which ought to result
from the supraposition in the seusorium of any two or more sensa-
tions which we may please to call primary ; so that if, following
common usage, I speak in what follows of red, yellow, and blue (or
in reference to Young's theory of red, green, and violet) &% j)rimary
colours, I refer only to the possibihty of producing all coloured sensa-
tions by the union on the retina of different proportions of lights,
competent separately to produce those colours, which is purely a
matter of experience.
It is necessary to premise this, when I remark that I by no means
regard as a logical sequence INIr. Pole's conclusion in § 15, that
because he perceives as colours only yellow and blue, therefore the
neutral impression resulting from their union must be that sensation
which the normal-eyed call green. On the contrary, I am strongly
disposed to believe that he sees white as we do, for reasons which I
am about to adduce.
Mr. Maxwell has lately announced his inability to form green by
the combination of blue and yellow. On the other hand, the pris-
matic analysis of the fullest and most vivid yellows (those which
excite the sensation of yellowness in the greatest perfection), as the
colours of bright yellow flowers, or that of the yellow chromate of
mercury, clearly demonstrates the fullness, richness, and brilliancy
of their colour to arise from their reflexion of the whole, or nearly
the whole of the red, orange, yellow, and green rays, and the sup-
pression of all, or nearly all the blue, indigo, and violet portion of the
spectrum. On the hypothesis of an analysis of sensation correspond-
ing to an analysis of coloured light, these facts would seem incom-
patible with the simplicity of the sensation yellow, and it would
appear impossible (on that hypothesis) to express them otherwise
than by declaring red and green to be primary sensations, and yellow
a mixture of them — a proposition which needs only to be understood
to be repudiated — quite as decidedly as that the sensation of green-
ness is a mixture of the sensations of blueness and yellowness, and for
the same reason ; the complete want of suggestion of the so-called
simple sensations by the asserted complex ones.
Mr. Maxwell's assertion that blue and yellow do not make green,
assuredly appears startling as contradictory to all common experience ;
but the common experience appealed to is that of artists, dyers, and
others in the habit of mixing natural colours as they are presented to
I
Sir J. F. W. Herschel on Colour- Blindness. 151
us in pigments, coloured tissues, &c., who have for the most part
never seen a prismatic spectrum, or at least attended to its phseno-
mena. The perceptions of colour aflforded by such objects are those
of white light from which certain rays have been abstracted by ab-
sorption, that is to say, they are negative hues, or hues of darkness
rather than of light, inasmuch as all the colouring of the artist is
based, not on the generation, but on the destruction of light. This
circumstance, which is not generally recognized, even among edu-
cated artists, has vitiated all the language of chromatics as applied to
art, and so placed a barrier between the painter and the photologist,
which has to be surmounted before they can come to a right under-
standing of each other's meaning. It is evident, that, to make
experiments on the svibject free from this objection, absorptive
colours must be discarded, at least in bodily mixture with each other.
Thus it is true that a dingy green may be produced by rubbing
together in powder prussian blue and the yellow chromate of mer-
cury above mentioned ; but both these agree in reflecting a con-
siderable, and the latter a very large proportion of green light, to the
predominance of which in the joint reflected beam its tint is owing.
So also, when blue and yellow liquids (not acting chemically on each
other) are mixed, as in water-colour drawings, greens, sometimes
very lively ones, are produced. In these cases the yellow absorbs
almost all the whole of the incident blue, indigo, and violet light, and
the blue a very large proportion of the red, orange, and yellow, both
allowing much green to pass ; 'and to this, rather than to a mixture of
the other rays, the resulting tint is due.
In the light transmitted by cuprate of ammonia of a certain thick-
ness, the red, orange, yellow, and green are wholly extinguished,
while the blue, indigo, and violet are allowed to pass. The result is
the fullest and bluest blue it is possible to obtain. From this result,
compared with that derived from the analysis of natural yellows, it
follows that the union on the retina of the yellowest yellow, and the
bluest blue, in such proportions that neither shall be in excess,(so as
to tinge the resulting light either yellow or blue, is not green, but
white. The same conclusion follows from dividing the spectrum
into two, the one portion containing all the less refrangible rays up
to the limit of the green and blue, the other all the remaining rays.
If the blue portiou be sup))ressed, and the remainder reunited by a
refraction in the opposite direction, the resulting beam is yelloiv, if
the other, blue, both vivid colours — but if neither, lohite of course,
and not green, results from the exact recomposition of the original
white beam.
It may be objected to this, that in the complementary colours
exhibiteil by doubly- refracted pencils in polarized light, yellow is
often found to be complementary to purple, and blue to orange.
But in neither of these pairs of colours is the spectrum divided in
the manner above indicated ; and, moreover, in many instances yellow
and blue are found as complementary colours in the oppositely
polarized j)encils ; of whicii examples will be found in the scale of
tints produced by sulphate of barytes in my paper " On the Action
of Crystallized Bodies in Homogeneous Light " (Phil. Trans. 1820,
153 Boyal Society : —
Table I.). " Rich yellow" appears also as opposed to " full blue"
in the scale of complementary tints exhibited by mica in my " Trea-
tise on Light" (Encyc, Metrop., art. 507). It is not asserted that
either a good yellow or a good blue cannot be produced otherwise
than in a particular manner, but that they ca7i be produced in that
particular manner, and that wheti so produced, their union affects
the eye with no sensation of greenness.
Let two very narrow strips of white paper, A, B, be placed parallel
to one another in sunshine, so as to be seen projected on a perfectly
black ground (a hollow shadow), and viewed through a prism having
the refracting edge parallel to them, the refraction being towards the
eye, and let the nearer B be gradually removed towards A, so that
the red portions of B's spectrum shall fall upon the green portion of
A's. Their union will produce yeJlovi, or, if too far advanced,
orange. On the other hand, it will be seen that the yellow space in
B's spectrum on which the blue of A's falls is replaced by a streak
of white, — whiteness, and not greenness, being the resultant of the
joint action of these rays on the retina. If the strips be made
wedge-shaped, taf)ering to fine points, and A being still white, B be
made of paper coloured with the yellow chromate of mercury before
mentioned, the whiteness of the streak where the blue of A mixes
with the yellow of B near the pointed extremities will be very
striking.
There is a certain shade of cobalt-blue glass which insulates, or
very nearly so, a definite yellow ray from the rest of the spectrum,
suppressing the orange and a great deal of the green. If the spec-
trum of B, formed and coloured as last described, be viewed through
this glass, a very well-defined image of it, clearly separated from its
strong red and very faint blue images, will be seen. As the glass in
question allows blue rays to pass, the white object. A, besides its
definite yellow image, will form a broad blue, indigo, and violet train
nearer to the eye. Now let B be gradually brought up towards A,
so that the violet, indigo, and blue rays of this train shall coincide in
succession with the yellow image of B, — no sensation of greenness ivill
arise at any part of its movement. Again, if a white card be laid
down on a black surface, the edge nearest the eye, when refracted
towards the spectator by a prism, will of course be fringed with the
more refrangible half of the spectrum. Let this be viewed through
such a glass, and in the blue space so seen introduce one half of a
narrow rectangular sli}) of paper thus coloured, having its upper edge
in contact with the lower edge of the white card, the other half pro-
jecting laterally beyond the card. In this arrangement the definite
image of the yellow paper insulated by the glass will be seen divided
into a yellow half, projecting beyond the blue fringe, and a purplish-
or bluish-white one within it, hardly to be distinguished from the
image of the white paper, of which it seems a continuation, and
which through the glass in question appears a pale blue. This same
purplish tint was observed to arise also under the following circum-
stances : — Laying down in a good diffused light a paper of an ex-
ceedingly beautiful ultramarine blue, and beside it, and somewhat
overlapping it, another coloured with the same yellow chromate, I
Sir J. F. W. Herschel 07i Colour -Blindness. 153
set upon the line of junction a sheet of glass inclined to the plane of
the papers upwards towards the eye, so as to allow the blue to be
seen by transmitted light, while the yellow reflected from the glass
was at the same time received into the eye. By varying the inclina-
tion of the glass, the yellow reflexion could be made more or less
vivid, so as either to be nearly imperceptible or quite to kill the
blue of the paper. But at no stage of its intensity, gradually in-
creased from one to the other extreme, was the slightest tendency to
greenness produced. The colour passed from blue to yellow, not
through green, but through a pale uncertain purplish tint, not easy
to describe, but as remote from green as could be well imagined.
Of course in all such experiments one eye only must be used.
Stereoscopic superposition of colour, which at first sight would ap-
pear readily available, does not satisfy the requisite conditions, and
yields no definite results.
The conclusions from these facts may be summed up as follows : —
1st. That in no case can the sensation of green be produced by the
joint action on the eye of two lights, in neither of which, separately,
prismatic green exists ; 2ndly. That the joint action of two lights,
separately producing the most lively sensations of blue and yellow,
does not give rise to that of green, even when one of them contains
in its composition the totality of green light in the spectrum;
and, 3rdly. That all our liveliest sensations of yellow are produced by
the joint action of rays, of which those separately exciting the ideas
of red and green form a large majority ; and that a decided yellow
impression is produced by the union of these only.
From these ])remises it would seem the easiest possible step to
conclude the non-existence of yellow as a primary colour. But this
conclusion I am unable to admit in the face of the facts, — 1st, that
a yellow ray, incajiable of prismatic analysis into green and red, may
be shown to exist, both in the spectrum and in flames in which soda
is present ; and 2ndly, that ncitlier red nor green, as sensations, are
in the remotest degree suggested by that yellow in its action on the
eye. Whether under these circumstances the vision of normal-eyed
persons should be termed trichromic or tetrachromic, seems an open
question.
That Mr. Pole's vision is f//chromic, however, there can be no
doubt. If I could ever have entertained any as to the correctness
of the views I have embodied of the subject in that epithet, after
reading all I have been able to meet with respecting it, this paper
would have dispelled it. That he sees blue as we do, there is no
ground for doubting ; and I think it extremely likely that his sensa-
tion of whiteness is tlie same as ours. AVhefher his sensation of
yellow corresponds to ours of yellow, or of green, it is impossible to
decide, thougli the former seems to me most likely.
One of the most remarkable of the features of tbis case, and in-
deed of all similar ones, is tlie feebleness of the efticacy of the red
rays of the s])ectrum in point of illuminating power, which certainly
very strongly suggests an explanation drawn from the theory of three
primary coloured species of light, to one of which the colour-blind
may be supposed absolutely insensible, Mr. Pole himself evidently
154 Royal Society : —
leans to this opinion. I had gatisfied myself, however, in the case
of the late Mr. Troughton, that the extreme red — that pure and de-
finite red which is seen in the solar spectrum only when the more
luminous red is suppressed, and in which I cannot persuade myself
that any yellow exists, was not invisible to him, — though of course not
seen as reef ; and on supplying Mr. Pole with a specimen of a glass,
so compounded of a cobalt-blue and a red glass as to transmit posi-
tively no vestige of any other ray, but that copiously, so that a
candle seen through it appears considerably luminous, and the
window-bars against a cloudy sky are well seen if other light be kept
from falling on the eye, — T am informed by him that he saw through
it " gas, ^re and other strong lights with perfect distinctness," and
that the colour so seen is a "very deep dark yellow." Now it seems
to me impossible to attribute this to any minute per-centage of yellow
light of the same refrangibility, which this can be supposed to con-
tain. The purity of its tint is extraordinary ; and its total intensity
so small, that supposing it reduced to one-tenth of its illuminating
power by the suppression of the whole of its primary red constituent,
I cannot imagine that any gas-flame or fire-light would be visible
through it, or any other luminous body but the sun.
Still it remains a fact, however explained, that the red rays of the
spectrum generally are to the colour-blind comparatively but feebly
luminous. Mr. Pole speaks of red in more places than one as "«
darkening power -y'^ and in the letter I have received from him in
reply to my query as to the visibility of light through the red glass
above mentioned, he insists strongly on its action as darkness. This,
however, can only be understood of the effects of red powders in
mixture, and not of red light ; and as, to our eyes, an intense blue
powder, such as prussian blue, has, besides its colorific effect, a vio-
lent darkening one (owing to its feeble luminosity), so, to the colour-
blind, red powders, when added to others, contribute but little light
in proportion to the bulk they occupy in the mixture, and therefore
exercise a darkening power by displacing others more luminous than
themselves. I think it therefore very probable that red appears to
the colour-blind as yellow-black does to the normal-eyed, or, in
other words, that our higher reds are seen by them as we see that
shade of brown which verges to yellow — that of the faded leaf of the
tulip-tree for instance. Now it is worthy of remark, that it is very
difficult for the normal-eyed to become satisfied that the browns are
merely shades of orange and yellow. Brownness (such at least has
always been my own impression) is almost as much a distinct sensation
as greenness ; so that I am not at all surprised at the expression in
§ 22, that the " sensation of red as a dark yellow is certainly very
distinct from full yellow," or that a colour-blind person should, after
long and careful investigation, arrive at the conclusion that red is
not to him a distinct colour. I find all this completely applicable
to my own perception of the colour brown.
Mr. Pole (§11) appears to lay great stress on the fact,'that in a
closed colour circle in which red, yellow, and blue are so arranged
that each shall graduate into both the others, there occurs in the
space where red and blue graduate into ea<;h other, •' a hue of red
Sir J. r. W. Herschel on Colour-Blindness. 155
T\-hich is to liim absolutely insensible," and that this red corresponds
7iof to that colour which, under the name of carmine, offers to the
normal-eyed the beau-ideal of redness, but what they term " crim-
son." Invisibility, as an element of colour, must not] here be con-
founded with invisibility as light. It is certain that he sees the
crimson. It is not to him black, but (just what it ought to be on
the supposition that his vision is dichromic, and the union of his
colours produces white) a neutral, obscure grey ; grey being only an
abbreviated expression for feeble illumination by white light. In a
circle coloured with three elements graduating into each other, there
is no neutral point — none, that is, where whiteness or greyness can
exist ; but when coloured with only two elements, such as yellow
and blue (posifive yellow and blue, that is, whose union produces
white, not green), there are of necessity two neutral points which
would be both equally white, i. e. ccpially luminous, if the two ex-
tremities of each of the coloured arcs graduated off by similar de-
srrees. But this not being the case with the vellow arc, one of its
ends to the colour-blind corresponding to a continuation of the red,
and so being deficient in illuminating power, the point of neutrality
will be that where a feebler yellow is balanced by a feebler blue, and
will therefore be less luminous, i. c. less white or more grey than
the other neutral spot. It is evident, from the general tenor of
Mr. Pole's expressions throughout this paper, that his ideas on
the subject of colour are gathered mainly from the study of pigments
and absorptive (i. e. negative) colours, and not from that of prismatic
(or positive) ones. In other words, his language is that of the
painter, as distinguished from the photologist ; the distinction con-
sisting in this — that in the former colour is considered in its con-
trast with whiteness, in the other with blackness ; and thus it is
that black is considered by many painters as an element of colour,
as whiteness necessarily is by photologists.
I may perhaps be allowed to add a few words as to the statistics
of this subject. Dr. Wilson gives it as the result of his inquiries,
that one person in every eighteen is colour-blind in some marked
degree, and that one in fifty-five confounds red with green. Were
the average anything like this, it seems inconceivable that the exist-
ence of the phenomenon of colour-blindness, or dichromy, should
not be one of vulgar notoriety, or that it should strike almost all
uneducated persons, when told of it, as something approaching to
absurdity. Nor can I think that in military operations (as, for in-
stance, in the placing of men as sentinels at outposts), the existence,
on an average, of one soldier in every fifty-five unable to distinguish
a scarlet coat from green grass would not issue in grave inconve-
nience, and ere this have forced itself into prominence by pro-
ducing mischief. Among the circle of my own personal acquaint-
ance I have only known two (though, of course, I have heard of
and been placed in correspondence with several) ; and a neighbour
of mine, who takes great delight in horticulture, and has a superb
collection of exotic fiowers, informs me that among the nniltitude of
persons who have seen and admired it, he does not recollect having
ever met with one who appeared incapable of appretiating the variety
156 Royal Socicfy : —
and richness of the tints, or insensible to the brilliancy of the nume-
rous shades of red and scarlet. It may be, however, that the per-
centage is on the increase — certainly we hear of more cases than
formerly ; but this probably arises from the fact of this, like many
other subjects, being made more generally matter of conversation.
In further reference to the question of the superposition of colours
in the spectrum, or of the intrinsic compositeness of rays of definite
refrangibilities, I may mention a phenomenon which I have been
led to notice in the prosecution of some experiments on the photo-
graphic impressions of the spectrum on papers variously prepared,
which appeared to me, ichen first noticed, quite incompatible with
the simplicity of those rays at least which occupy the more luminous
portion of the spectrum, extending between the lines marked D and E
by Fraunhofer, and clearly to demonstrate the presence of green
light over nearly the whole of that interval. In these experiments
the spectrum formed by two Fraunhofer flint prisms, arranged so as
to increase the dispersion, and adjusted to the position of least de-
viation for the yellow rays, was concentrated by an achromatic lens,
and received on the paper placed in its focus, which could be viewed
from behind. A series of white papers impregnated with washes of
various colourless or very slightly coloured chemical preparations,
and dried, were exposed ; and the spectrum being received on them,
and the centre of the extreme red image as viewed through a stand-
ard glass, adjusted to a fiducial pinhole ; a sensitizing wash of nitrate
of silver, or any other fitting preparation, was copiously applied to
the exposed surface while under the action of the light. Now, under
these circumstances, I uniformly found that whereas the spectrum
viewed from behind through the paper exhibited all over the space
in question a dazzling very pale straw-yellow, hardly distinguishable
from white, yet as the photographic action proceeded, and the
translucency of the paper began to be somewhat diminished also by
incipient drying, very nearly the whole of that space became occu-
pied by a full and undeniable green colour, so as to give the idea of
a distinctly four-coloured spectrum — red, green, blue, and violet ;
the yellow being in some instances almost undiscernible, and in
others limited to a mere narrow transitional interval rather orange
than yellow. It was at the same time evident that a great extinction
of light (illumination independent of colour) had also been operated,
the vivid glare of the part of the spectrum in question being reduced
to a degree of illumination considerably inferior to the red part, or,
at all events, not much superior. The change of colour was far
greater than could be attributed to any effect of contrast, and was
proved decisively not to be due to that cause by hiding the adjacent
red and blue when the green remained unaffected in apparent tint.
When, for the photographic preparations wetted as described,
ordinary, dry, coloured papers were substituted, the change of colour
in question was always produced whenever the thickness of the paper
and its absorptive power were not such as to destroy or very much
enfeeble the more refrangible light. Taking, as a term of compa-
rison, a ])urely white, wove, writing-paper, I found that the substi-
tution of writing-paper, tinted with the ordinary cobalt blue com-
Sir J. F. W. Herschel on Colour-Blindness. 157
monly met with, sufficed to give a very great extension of the green,
almost to the extinction of the yellow, while, when the papers used
were pale-yellow or clay-coloured, answering to the tints called
"buff" or "maize" (nearly approximating to Chevreul's orange
A and 3), and which might naturally have been expected to transmit
yellow rays more abundantly at all events than the blue, the spectra
(viewed at the back of the papers) were particularly full and abun-
dant in green, occupying the whole of the debateable ground. In
the case of the former, a narrow yellow space was seen, and the blue
was very much enfeebled, and separated from the green by a very
perceptible suddenness of transition. "NTith the latter the green was
finely exhibited, and the yellow confined to a narrow orange-yellow
border : the blue and violet much enfeebled.
On further considering these facts, there seemed to be but three
ways of accounting for them : — 1st, by the effect of contrast. This
I consider to ,be disposed of by the suppression of the adjacent
colours, as recorded above. 2udly, by extinction of a yellow element
of colour over the space DE, allowing a substratum of green to sur-
vive ; or, which comes to the same, by the extinction of the red ele-
ment over the same space, which, by its combination with (an as-
sumed elementary) green, produced the original brilliant straw-yellow.
And 3rdly, by admitting as a principle, that our judgment of colours
absolutely, in se, and independent of contrast, is influenced by the
intensity oi the light by which they afllect the eye, and that very
vivid illumination enfeebles or even destroys the perception of
colour. As the apparent change of colour from pale-yellow to green
in the cases above related was always accompanied ^^ith a great
diminution of general intensity, it occurred to me to produce such
diminution by optical means, which should operate equally on all the
coloured rays, and diminish all their intensities in the same ratio.
This was accomplished by viewing the spectrum (as projected on
purely white paji^;) by reflexion on black glass, or by two successive
reflexions in different planes, and I found the very same effect to
take ])lace. That })ortion DE of the spectrum which in the unre-
flected state appeared dazzlingly bright and nearly colourless, was
seen by one such reflexion, and still more so by two, green. The
extension of the green region was greater, and the limitation of the
yellow portion more complete, according to the amount of illumina-
tion destroyed by varying the angles of incidence on the glasses.
When much enfeebled by two cross reflexions, the aspect of the
spectrum was that represented in Chevreul's coloured picture of it
from the line A to II. When enfeebled by other means, as by view-
ing the spectrum thrown on a blackened surface, the effect was
exactly the same.
The last of oiu* three alternatives, then, would appear to be esta-
blished as the true explanation ; and in respect of the second, it is
eliminated by the consideration that neither the slight degree of
coloration in the bluish pajiers, or the tint of the pale-yellow ones
which effected the change, would give rise to so great a preferential
extinction of yellow or red rays as an explanation founded on that
alteruative would reciuirc. The phcuomeuou is certainly a very
158 Geological Society : —
striking one, and has created great surprise in those to whom I have
shown it.
GEOLOGICAL SOCIETY.
[Continued from p. /S-]
December 14, 1859. — Prof. J. Phillips, President, in the Chair.
The following communications were read : —
1. "On some Remains of Polyptychodon from Dorking." By
Prof. Owen, F.R.S., F.G.S.
Referring to the genus of Saurians which he had founded in 1841
on certain large detached teeth from the Cretaceous beds of Kent
and Sussex, and which genus, in reference to the many-ridged or
folded character of the enamel of those teeth, he had proposed to
call Polyptychodon, Prof. Owen noticed the successive discoveries of
portions of jaws, one show'ing the thecodont implantation of those
teeth, w^hich, with the shape and proportions of the teeth, led him to
suspect the crocodilian affinities of Polyptychodon ; and the subse-
quent discovery of bones in a Lower Greensand quarry at Hythe,
which, on the hypothesis of their having belonged to Polyptychodon,
had led him to suspect that the genus conformed to the Plesio-
sauroid type.
The fossils now exhibited by Mr. G. Cubitt of Denbies, consisted
of part of the cranium (showing a large foramen parietale), frag-
ments of the upper and lower jaws, and teeth of the Polyptychodon
interruptus, from the Lower Chalk of Dorking, nnd afforded further
evidence of the plesiosauroid affinities of the genus. Professor Owen
remarked that in a collection of fossils from the Upper Greensand
near Cambridge, now in the Woodwardian Museum, and in another
collection of fossils from the Greensand beds near Kursk in Russia,
submitted to the Professor's examination by Col. Kiprianoff, there
are teeth of Polyptychodon, associated with plesiosauroid vertebrae
of the same proportional magnitude, and with portions of large limb-
bones, without medullary cavity, and of plesiosauroid shape.
Thus the evidence at present obtained respecting this huge, but
hitherto problematical, carnivorous Saurian of the Cretaceous jjeriod
seemed to prove it to be a marine one, more closely adhering to the
prevailing type of the Sea-lizards of the great mesozoic epoch, then
drawing to its close, than to the Mosasaurus of the Upper Chalk,
which, by its vertebral, palatal, and dental characters, seemed to
foreshadow the Saurian type to follow.
Prof. Owen exhibited also drawings of specimens in the Wood-
wardian Museum and in the Collection of Mr. W. Harris, of Charing,
which show the mode and degree of use or abrasion to which the
teeth of Polyptychodon had been subject.
2. " On some Fossils from near Bahia, South America." By
S. Allport, Esq.
The south-west point of the hill on which the Fort of Montserrate
is built, in Bahia Bay, exhibits a section of alternating beds of con-
glomerate, sandstone, and shale ; in the last Mr. Allport discovered
Mr. J. W. Dawson on Fossils fi-om Nova Scotia. 159
a large Dinosaurian dorsal vertebra, not unlike that of Megalosaurus,
several Crocodilian teeth, and numerous large scales of Lepidotus,
together with a few Molluscs (Paludina, Unio, &c.), some Ento-
mostruca, and Lignite. Two miles from Montserrate, in a N.E.
direction, is the Plantaforma, another hill of the same formation, but
loftier. The shales here also yielded similar fossils.
These fossiliferous shales and conglomerates dip to the N.W.
towards the Bay, and appear to overlie a similarly inclined whitish
sandstone, which rests against the gneissose hills ranging north-
eastwardly from the point of St. Antonio.
3. " On a Terrestrial Mollusc, a Chilognathous Myriapod, and
some new species of Reptiles, from the Coal- formation of Nova
Scotia." By J. W. Dawson, LL.D.. F.G.S. &c.
On revisiting the South Joggins in the past summer, Dr. Dawson
had the opportunity of examining the interior of another erect tree
in the same bed which had afforded the fossil stump from which the
remains of Dcndrerpeton Acadianum and other terrestrial animals were
obtained in 1851 by Sir C. Lyell and himself. This second trunk
was about 15 inches in diameter, and was much more richly stored
with animal remains than that previously met with. There were here
numerous specimens of the land-shell found in the tree previously
discovered in this bed ; several individuals of an articulated animal,
probably a Myriapod ; portions of two skeletons of Dendrerpeton ;
and seven small skeletons belonging to another Reptilian genus,
and probably to three species.
The bottom of the trunk was floored with a thin layer of carbonized
bark. On this was a bed of fragments of mineral charcoal (having
Sigillarioid cell- structure), an inch thick, with a few Reptilian bones
and a Sternberg ia-c&st. Above this, the trunk was occupied, to a
height of about 6 inches, with a hard black laminated material,
consisting of line sand and carbonized vegetable matter, cemented by
carbonate of lime. In this occurred most of the animal remains,
with coprolites, and with leaves of Noeggerathia {Poacites), Carpo-
lithes, and Calamites, also many small pieces of mineral charcoal
showing the structures of Lepidodendron, Stigmaria, and the leaf«
stalks of Ferns. The u])per part of this carbonaceous mass alter-
nated with fine grey sandstone, which filled the remainder of the
trunk as far as seen. The author remarked that this tree, like other
erect Siyilluri<e in this section, became hollow by decay, after having
been more or less buried in sediment ; but that, unlike most others, it
remained hollow for some time in the soil of a forest, receiving small
quantities of earthy and vegetable matter, falling into it, or washed in
by rains. In this state it was probably a place of residence for the
snails and myriapods and a trap and tomb for the reptiles ; though
the jiresence of coprolitic matter would seem to show that, in some
instances at least, the latter could exist for a time in their under-
ground prison. The occurrence of so many skeletons, with a hundred
or more specimens of land-snails and myriapods, in a cylinder only
15 inches in diameter proves that these creatures were by no means
rare in the coal-forests ; and the conditions of the tree with its air-
160 Geological Society : —
breathing inhabitants implies that the Sigillarlan forests were not
so low and wet as we are apt to imagine.
The little land-shell, specimens of which with the mouth entire
have now occurred to the author, is named by him Pupa vetusta.
Dr. Dawson found entire shells of Physu heterostropha in the stomach
of Menobranchus lateralis, and hence he supposes that the Pvpce may
have been the food of the little reptiles the remains of which are
associated with them.
Two examples of Spirorbis carbonurius also occurred ; these ma\
have been drifted into the hollow trunk whilst they were adherent
to vegetable fragments. The Myriapodis na.med Xylobius Sigillariee,
and is regarded as being allied to lulus.
The reptilian bones, scutes, and teeth referable to Dendrerpelon
Acadiamnn bear out the supposition of its Labyrinthodont affinities.
Those of the new genus, Hylonomus, established by Dr. Dawson on
the other reptilian remains, indicate a type remote from Archegosaurvs
and Labijrinthodon, but in many respects approaching the Lacertians.
The three species determined by the author are named H. Lyellii,
H. aciedentatus, and H. Wymani.
4. " On the Occurrence of Footsteps ofChirotherium in the Upper
Keuper of Warwickshire." By the Rev. P. B. Brodie, F.G.S.
True ('hirotherian footsteps do not appear to have been hitherto
met with in the Keuper of Warwickshire ; but a specimen of Keuper
sandstone showing the casts of a fore and a hind foot of Chirotherium
■was lately turned up by the plough at Whitley Green near Henley-
in-Arden. The breadth of the fore foot is about 2 inches ; the hind
foot is 4| inches across. As the New Red sandstone of Cheshire, so
well known for its fine Chirotherian foot- tracks, certainly belongs to
the upper part of the New Red series, it may now be further corre-
lated with the Upper Keuper of Warwickshire, the latter having
yielded true Chirotherian foot-prints.
January 4, 1860. — Prof. J. Phillips, President, in the Chair.
The following communications were read : —
1. " On the Flora of the Silurian, Devonian, and Lower Carboni-
ferous Formations." By Prof. H. R. Goeppert, For. Mem. G. S.
The number of all the fossil plants which the author has described
as belonging to these formations (chiefly from Germany) amounts
to 184 species: Algse, 30 species; Calaminere, 20 ; Asterophylliteae,4;
Filices, 64; Stlaginese, 39; Cladoxylese, 4; Noeggerathise, 8; Sigilla-
riae, 6; Coniferae, 6; Fruits (uncertain), 3.
Prof. Goeppert has seen only Algce from the Silurian Rocks.
Sigillaria Hausmanni is one of the most interesting of the Lower
Devonian plants, and Sagenariu Jl^eltheimiana of the Middle Devo-
nian. 'J'he Upper Devonian has several terrestrial plants. Of the
Lower Carboniferous Flora, the following are the most important and
characteristic plants : — Culamites Trunsitionis, C. Roemeri, and Sage-
naria Weltheimiana. The last name supersedes Knorria imbricata.
2. " On the Freshwater Deposits of Bessarabia, Moldavia, Walla-
chia. and Bulgaria." By Capt. T. Spratt, R.N., C.B., F.R.S., F.G.S.
Capt. Spratt first referred to the many isolated patches of fresh-
Capt Spratt on the Freshwater Deposits of Bessarabia, ^c. 161
water deposits in the Grecian Archipelago and in the neighbouring
countries, also around the Black Sea, to which others have alluded,
or which have been described hy himself as evidences of the existence
of a great freshwater lake, probably of middle tertiary age.
On the borders of the Yalpuk Lake, in Southern Bessarabia, are
sections exhibiting old lacustrine deposits containing similar fossils
to those found elsewhere by Capt. Spratt in the strata referred by
him to the extensive oriental lake of the middle tertiary period.
Among these fossils are freshwater Cockles ; such as are associated
with Dreissena polymorpha in the strata at the Dardanelles and
elsewhere. After some search, Capt. Spratt found similar Cockles
living in the Yalpuk lake ; and from this evidence, and from the
relatively different levels of the old lacustrine deposits and the
present Black Sea, he satisfied himself of the really freshwater
condition of the old tertiary lake, — the Black Sea area having been
separated from the old lacustrine area of Bessarabia and the Pro-
vinces by a barrier at the Isaktcha hills which the Danube has since
cut through. Capt. Spratt remarked that the lacustrine conditions
of the great area in Eastern Europe and Asia Minor where he has
indicated freshwater deposits were probably interfered with by
volcanic outbursts, which opened a communication between the
Euxine and Mediterranean, altering the levels of the region, causing
the formation of the great gravel-beds at the foot of the Caipathians,
and an outspreading of the brown marly superficial deposits of the
Steppe, which are locally impregnated with mineral or marine salts,
indicative either of the influx of the sea, or of mineral solutions set
free by volcanic agencies.
Capt. Spratt also described the older rocks, some probably of
Triassic age, and others Cretaceous, which are here conformably
overlain by the lacustrine deposits. These he saw in the hills,
south of the Danube, near Tultcha and Beshtepeh ; also at the
Raselm Lagoon, where Cretaceous shales and marble containing
Ceratites, &c. occur; the latter at Popin Island. At Dolashina, a
cape south of the Raselm Lagoon, the soft Cretaceous limestone is
full of small Inocerami.
These indications of Secondary rocks are intimately connected
with those further south, at Cape Media and Kanara, formerly
described by the author.
3. " On the Recent and Fossil Foraminifera oi the Mediterranean
Area." By T. Rupert Jones, F.G.S., and W. K. Parker, Mem.
Micr. Soc.
The authors presented an extensive Table of the Species and
varieties of recent Foraminifera from several localities in the Medi-
terranean (worked out from material gathered and dredged by Capt.
Spratt, Mr. Hamilton, Prof. Meneghini, and other friends), and of
the fossil forms from the Tertiary deposits of Malaga (Spain), Turin,
Sienna, Palermo, and Malta (communicated by Prof. Ansted, Prof.
Meneghini, and the Marchese C. Strozzi, or supplied from the
Society's Museum) ; also the fossil Foraminifera from Baljik supplied
by Capt. Spratt, and those of the Vienna Basin as elaborated by
D'Orbigny, Czjeck, and Reuss. TherecentForawjHi/I?;-a, tabulated
Fhil. Mag. S. 4. Vol. 19. No. 125. Feb. 1860. ' M
162 Intelligence and Miscellaneous Articles.
in eleven columns, were illustrative of the range of the respective
species and varieties in different zones of sea-depth, from the shore
to 1700 fathoms, and of the relative size of the individuals, and of
their proportional paucity or abundance. Among the seventeen
columns of fossil Foraminifera, some were very rich in species and
varieties, especially in the case of the Siennese clays, the Malaga
clay, and the Vienna basin. From the evidence afforded by the com-
parison of the fossil with the recent Foraminifera, the Siennese blue
clays of S. Cerajolo, S. Donnino, S. Lazaro, and Coroncino were
regarded as having been deposited in various depths of from 40 to
100 fathoms; so also the clay-beds of Malaga and of the Vienna
basin. A blue clay from S. Quirico was probably formed in about
200 fathoms ; a blue clay from Pescajo, on the contrary, was the
deposit of a shallow estuary. A sand from Pienza, and others from
Montipoli, Castel' Arquato, and San Frediano, contain Amphistegina,
and were probably deposited in from 10 to 20 fathoms water. As
the Amphistegina appears now to be extinct as regards the Medi-
terranean, these Amphistegina-beds, and others at Palermo and in
the Vienna Basin, may be of miocene age. Another Siennese clay
from Monti Arioso is of shallow-water formation. From Turin some
shelly sands, of pliocene age, were defined as containing a group of
Foraminifera similar to those now living on the western shores of
Italy ; and the Palermo deposits are, for the most part, not very
dissimilar. The Heterostegina-bed at Malta, formed probably in
rather shallow water, is characterized by a species now absent from
the Mediterranean. The tertiary deposit from Baljik appears to
have been a shallow-water deposit, characterized by some forms
peculiar at the present day to the Red Sea, — a condition that is also
indicated by some of the Viennese deposits.
XXI. Intelligence and Miscellaneous Articles.
OPTICAL LECTURE-EXPERIMENTS. BY PROF. KNOBLAUCH.
DID I not hope to furnish my colleagues with a few welcome
experiments for the lecture table, I should scarcely venture
to occupy these pages with a communication which involves nothing
but what has been long well known.
Optical lenses have been so universally constructed of substances
whose indices of refraction exceed that of the surrounding medium
(such being alone useful in practice), that, accustomed to the phaeno-
mena dependent thereupon, we unconsciously associate convergent
effects with convex, and divergent ones with concave lenses.
In order strikingly to illustrate by experiment the influence which
here, under the same form of the limiting surfaces, the enclosed
medium exerts, I introduce, in my lectures on experimental physics,
experiments with hollow lenses so composed of plane glass discs and
watch-glasses, that the one forms a plano-convex, the other a plano-
concave lens*.
* The radius of curvature here is about 116 millims.; the aperture of
the setting has a diameter of about 64 millims.
Intelligence and Miscellaneous Articles. J 63
After filling both lenses with water, the first is used in a dark
room to obtain all the phsenomena presented by the objective collec-
tion, behind the lens, of all the luminous rays which pass through
the same : for instance, the principal focus is determined, and the
displacement of the same by the approach of a luminous point is
shown ; this displacement is continued until the rays leave the lens
in parallel directions, and subsequently the objective focus becomes
a virtual one. When the luminous point is replaced by a luminous
object, the convex water-lens also presents the series of diminished,
equal, and magnified inverted images, and at sufficiently small di-
stances of the object, the magnified uninverted virtual images.
The concave water-lens presents in air the simple phsenomena of
a diverging lens. It serves to demonstrate that, for every distance
of the luminous point, the rays diverge on leaving the lens, that the
foci are in consequence all virtual ones, and that in all cases dimi-
nished uninverted images are alone observed.
If the media in question are now interchanged, that is to say, if
the lenses are filled with air and surrounded by water, the optical
phsenomena, as may be easily seen, will be all reversed.
The convex lens will become a diverging one with a virtual prin-
cipal focus, whose distance from the lens may be easily measured
(according to Eisenlohr's method) by receiving upon a white screen
the divergent solar rays proceeding from the lens in such a manner
that the illuminated surface has a diameter double that of the lens.
The distance of the screen from the lens will then be equal to the
principal focal distance*. All objects (e. g. flame of a candle) behind
the lens now appear diminished in the same manner as we usually
find them to be with a concave glass lens.
The concave air-lens, however, has now under water become a
converging lens, whose principal focal length may be found by im-
mediately ascertaining the point of convergence of incident solar
rays. By means of a white screen immersed in the water, the course
of the rays before and after convergence may be clearly followed, and
the change of position of the focus, with changing distances of the
luminous point, easily provedf. A piece of ground glass, protected
from contact with the water by a second glass, is better than a non-
transparent white screen for receiving the objective inverted images :
for the screen can only be regarded from above, and the images upon
it appear to be raised and distorted ; whilst the ground glass can be
looked at from behind, whence the images appear both sharp and un-
* I employ a similar method in catoptrics iu order to measure the prin-
cipal focal distance of a convex mirror. Thus between the mirror and the
suu, and perpeiuUcular to the ra} s from tlie latter, is placed a screen in
which is a circular hole cciiial in magnitude to the portion of the mirror
required to be operated iii)ou ; around the hole, and concentric with it, is
described a circle of double its diameter on the si«lc of the screen facing
the mirror. VA'hcn the screen is so placed that the reflected rays exactly
Kll this circle, its distance from the mirror is equal to the required distance
of the virtual focus.
t If it were required to surround the luminous point uitli water, the
tlectrie light between coal-points might be used.
V. '2
164 Intelligence and Miscellaneous Articles.
changed when the eyes are on the same level and look through the
transparent sides of the box containing the water*. After illus-
trating in this manner the changing magnitude of the images, the
objective foci may be made to pass into virtual ones, and the corre-
sponding uninverted magnified images will make their appearance.
The agreement between convex lenses of water surrounded by air,
and concave lenses of air in water, maybe followed further by distin-
guishing the central and circumferential rays. So long as the foci
remain objective, the circumferential rays intersect nearer to the
lens than the central ones, but further from it when the foci are
virtual. With the concave water-lens surrounded by air, and the
convex air-lens in water, the foci are all virtual, and those of the cir-
cumferential rays are always nearer to the lens than the foci of the
central rays.
Although all this is easily explained by the simple laws of refrac-
tion, it was always instructive and surprising to spectators to observe
how a mere change of medium converts a diverging lens into a burn-
ing glass, and a microscope into a telescope.
To complete the above experiments, the action of a concave lens
may be destroyed by a convex one on placing one behind the other
in the water ; or if, instead of being all equal, the curvatures of the
lenses be properly adjusted, a Galilean telescope or a Briicke's mag-
nifier may be constructed with a concave object-glass and a convex
eyepiece.
The consequences of the above phsenomena of refraction, relative
to the phsenomena of reflexion which present themselves with water-
lenses in air and air-lenses in water, also hold good.
These hollow lenses, too, serve to compare with each other the
several effects presented by differently refracting bodies, such as
water and clove-oil, with the same form of lens in diflferent media. —
Poggendorff's Annalen, vol. cvii. p. 32.3.
ON THE FIXATION OF THE MAGNETIC IMAGE. BY M. J. NICKLI^S.
The name of magnetic image is given to the appearance observed
when iron filings are placed on a paper screen over the poles of a
powerful magnet. It may be fixed in the following manner : — A
sheet of waxed paper is placed over the poles of a powerful magnet,
and kept in its position by means of a screen interposed between
the paper and the poles. The image is then developed in the usual
way ; and when this is efi'ected, a hot brick or crucible cover is
brought near enough to melt the wax. The melted wax by capil-
larity penetrates the agglomeration of filings, just as water penetrates
a mass of sand. It is necessary that the layer of wax have a con-
siderable thickness, in order to be sufficient for the action of capil-
larity. On cooling, the wax retains the filings in their place, and
they present the same appearance as if still under the influence of
the magnet. — Comptes Rendus, Nov. 27, 1859.
* This box is 1 metre long, 1"'^ millims. hioh. and 110 millims. broad.
THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
MARCH 1860.
XXII. On certain Laws of Chromatic Dispersion.
By MuNGo Ponton, F.R.S.E.'^
THE attempts hitherto made to determine the laws of chro-
matic dispersion have generally proceeded on the principle
of assuming a certain law, and endeavouring, on its basis, to con-
struct a universal formula, which shall render it possible, from
having given the refractive indices of two or three of the fixed
lines of the spectrum for any medium, to find those of the
remainder. These attempts are known to have been attended
with but imperfect success.
It has accordingly been deemed expedient to adopt a difi'erent
course, — to assume the indices of all the seven fixed lines for
every refracting medium that has been examined, to bo, as deter-
mined by observation, nearly correct ; to analyse and compare
these indices with a view to discover the hidden law or laws
which they involve ; and, the general nature of these laws liaving
been thus brought to light, then to make on the observed indices
such corrections as may be required to bring them into strict
agreement with the laws so ascertained. Thus, without assu-
ming any one or more of the observed indices to be absolutely
accurate, as in the former method of proceeding, it may be found
possible so to correct each index as to obtain results harmo-
nious in themselves, and all agreeing with determinate general
laws. The following is a brief outline of the results to which
this method of research has led.
The most general formula under which tlie law of chromatic
dispersion can be expressed is the following. Let U represent
* Communicated by the Author, having been read before the British
Association at Aberdeen, September 1859.
Phil, May. S. 4. Vol. 19. No. 13C. March 18G0. N
166 Mr. M. Ponton on certain Laws
the length of undulation corresponding to a luminous wave that
should occupy the place of any one of the fixed lines of the
spectrum in the free aether, as determined by Praunhofer's
method of transmitting a divergent beam through a system of
fine equidistant lines so as to obtain chromatic dispersion with-
out refraction. Let /u, be the refractive index of this undulation
in any medium. Call — =u the length of the undulation within
the medium after refraction. Then the relation between U
and u may be expressed by the general formula a + x=u;
or conversely, €{u + a + x)=V. Here the quantities e and a are
constant for the same medium and temperature, being the same
for all undulations. The quantity x, again, which is compara-
tively minute, is peculiar to each wave, the medium and tempe-
rature remaining the same. It is not, however, a mere irregular
fragment applied either to remove an excess or supply a defi-
ciency, but it is subject to symmetrical laws to be hereafter ex-
plained. Suffice it meanwhile to state that these variable quan-
tities, represented by x, added to, or subtracted from each wave-
length, constitute the hrationality of the spectrum.
Save for these small quantities, every spectrum formed by a
refracting medium would present the same appearance as the
spectrum formed by transmitting a divergent beam through a
system of equidistant fine lines. The fixed lines of the spectrum,
whatever might be their actual distances, would preserve the
same relative mutual distances. The above formula would thus
assume the yet simpler form of « = w, or e (m + «) = U. There
would then be no irrationality in the various spectra ; and the
constant relations of the fixed lines B, C, D, &c. to the same
lines when refracted, or to h, c, d, &c., would always be
B-C , C-D , B-D , ^
=o — c, =c—a, =.b — a,
€ e e
and so on.
In every refracting medium, however, the fixed lines are more
or less exti'uded or thrust out of the places which they occupy in
the unrefracted spectrum, and their mutual distances are altered ;
so that the above relation no longer subsists. This extrusion
constitutes the irrationality, and every medium accordingly pos-
sesses an extrusive power besides its refractive and dispersive
powers.
To study the laws by which these several powers are governed,
it is needful to separate the efi"ects due to each, and especially, in
the first place, to ehminate the quantity x from the formula with
of Chromatic Dispersion. 167
a view to determine the constants e and a. Seeing that, in the
absence of x, the difference between the wave-lengths correspond-
ing to any two fixed lines before refraction, when divided by the
difference between those same two wave-lengths within the
refracting medium, would always be equal to e, it follows that,
by taking the whole of the fractions which may be thus formed,
we shall obtain as many values of e as there are fractions ; and by
taking the average of all these, the effects produced on the value
of e by the variable quantity x will be mutually neutralized.
Hence, by taking the sum of the 21 differences between the
wave-lengths corresponding to the seven fixed lines before re-
fraction (or as they exist in the unrefracted spectrum), and
dividing them by the sum of their 21 differences within the
refracting medium, the quotient will be e. The wave-length
within the medium is found by dividing each normal wave-
length by its own refractive index; so that, (j, being the index,
T> n
we have —=b, —=c, &c. In this manner the positive and
. ^. . '^
negative extrusions are made to neutralize each other. The pro-
cess, however, may be shortened thus :
(3B + 2C + D)-(F-f2G + 3H)_
{Sb + 2c + d)- {f+2ff + 3h) -'-
The numerator of this fraction is of course constant for all media,
and its denominator varies with the refractive indices.
The constant e having been thus found, a may be easily de-
termined as follows. Call B + C+D + E + F-f-G + H = S, which
is of course constant. Call b + c-\-d+e+f+ff + h = s,vfhich.wi\\
S
s— — *
vary with the indices. Then is — - — - = a, or -- -■ = a.
The two constants e and a having been thus determined, it is
easy to find a second series b^^, c^, dc^, &c., showing what the
wave-lengths within the medium would be, apart from their ex-
trusions; that is, if the fixed lines retained the same relative
mutual distances within the medium as they present in the
unrefracted spectrum. This series is obtained by the formula
6 e e
In this series, bc^, c.t, d^, &c., the following relations constantly
subsist: €{b^ — c^)='\i — C, e(c2— ^^2) = ^ — D, and so of the others.
Then the differences between b and bo, between c and c^, between
d and d^, &c. are the extrusions. In this manner the extrusion
due to each of the fixed lines may be ascertained in all those media
whose seven indices have been observed with sufficient accuracy j
N2
168
Mr. M. Ponton on certain Laws
and this having been accomplished, the mutual relations of these
extrusions, whether in the same or in different media, and the
laws by which they are governed, may be advantageously studied.
This is indeed the most important branch of the inquiry ; for
unless it can be shown that the extrusions follow some determi-
nate law, the general formula becomes indefinite.
A careful analysis and comparison of the extrusions of the
fixed lines in various media have brought to light the following
general principles and laws.
The extrusive power of a medium may in every case be defined
to be '' a property in virtue of which the medium transfers a
small portion of motive energy from one part of the spectrum to
another.^'
The media hitherto examined may be distinguished into two
great classes — Regular and Peculiar, the former being consider-
ably the larger of the two. As all media, however, are greatly
aff'ected by temperature, it may sometimes happen that a medium
may be regular at one temperature and peculiar at another.
These two classes shall be separately considered and described.
The following is a list of all the regular media hitherto ex-
amined : —
Solution of Nitrate of
bismuth.
Water.
Sol. Subacetate of lead.
Sol. Nitrate of mercury.
Sol. Sulphate of soda.
Sol. Muriate of baryta.
Sol. Superacetateoflead.
Sol. Nitrate of potash.
Sol. Sulphate of mag-
nesia.
Calcareous spar, both
rays.
Oil of sassafras.
Sol. Nitrate of lead.
Sol. I\Iiu-iate of am-
monia.
Nitric acid.
Sol. ]\Im'iate of lime.
Sol. Potash.
Oil of turpentine.
Oil of anise, temj). 20°
and 13°.
Creosote.
Crown-glass.
Rock-salt.
Arragonite, three axes.
Quartz, both rays.
Sidphuret of carbon.
Flint-glass.
Topaz, three axes.
In all regular media the transfer of motive energy takes place
from the terminal to the central parts of the spectrum ; and they
are therefore medio-posifive. The undulations corresponding to
the lines D, E, and F are always quickened by the extrusive force ;
consequently their wave-lengths within the medium are length-
ened. Hence for these three the formula is always a + cc = u.
On the other hand, the undulations corresponding to the fixed
lines B, C, G, and H are always retarded, or their wave-lengths
within the medium are shortened. Hence for these four the
formula is a—x = u. In every case the motive energy gained
by the one set of waves is exactly balanced by the loss sustained
by the others ; so that the sums of the positive and negative ex-
of Chromatic Dispersion. 1 69
trusions being each denoted by X, these two quantities arc always
equal, and 2X may be regarded as the measure of the extrusive
power of the medium. This, which may be called "the law of
equal transference/^ is the first to be recognized ; and it is found
to prevail in all media whatever, whether regular or peculiar.
From the above it follows that every regular medium presents
two nodal points, at which the extrusion passes from positive to
negative, or vice versa — the upper node lying between C and JD,
the lower between F and G. At these nodes the extrusion is nil.
The second law may in all regular media be expressed as fol-
lows: 3Z>j.-f 2cj— c(i.=3//j. + 2yj.— /^. It is proposed to call this
the " semel-bis-ter law.^^
From these two laws may be deduced the following general
formula for expressing the extrusive power of a medium :
--(Q + «±2X)=0.
The two quantities K and Q have diflferent values according as
the medium is regular or peculiar. In the former,
K=(B + C + G+H)-(D + E + F),
and is constant for all regular media. In these, also,
(^=[h + c^-g^h)-[d+e+f);
so that the value of Q varies with the medium and temperature.
The alterations in the constitution of these two quantities pre-
sented by peculiar media will be afterwards explained.
The third law governing the extrusions is as follows : — If these
be taken in pairs equidistant from the centre e^, and if the differ-
ence betsvcen h^ and li^c be denoted by Sj, that between Cj. and y,
by S2> ^i^d that between d^ and/,, by S3, then the differences be-
tween each pair of these three quantities 8j, 82, and 83 will con-
stitute a progression of the form ^, 2^, 3^, the quantity ^vary-
ing with the medium and temperature. This it is proposed to
call " the law of the equicentral common difference.^' The
varieties which this law presents are interesting; and it is im-
portant, as furnishing the means of detecting and correcting
slight cri'ors of observation.
There is yet a fourth law, which may be termed "the law of
coincident nodes;" but for the understanding of its nature, a
little explanation is required.
The series of internal wave-lengths b^, c^, d^, based on the
supposition of the medium being destitute of extrusive power,
havinc: been calculated from the formula
'C5
B , C
a = 0.y, a = fa, Kc.
€ € ^
170 Mr. M. Ponton on certain Laws
the series of refractive indices corresponding to it may be found
from the formula
and so on. This series of indices, '"^B, '^'C, &c., is that which
the medium would present had it only a refractive and disper-
sive, but no extrusive power. The differences between the ob-
served indices and this second series show what portion of the
former is due to the extrusive power of the medium. The posi-
tive and negative quantities do not here balance each other, as
in the case of the wave-lengths ; nor do they, like the extrusions,
exhibit any symmetrical arrangement ; but they present nodes
corresponding to those of the extrusions. It might a priori be
expected that this correspondence would be quite exact. It will
accordingly be found to be very nearly so in every case, taking
the indices as given by observation, or after having been subjected
to the corrections required by the third law ; and where the co-
incidence is not perfect, the difference is generally traceable to
the defects of decimal calculation. There can therefore be no
doubt of its being a general law that these two sets of nodes
ought exactly to correspond ; that is, the refractive indices of
the nodes, deduced from the extrusions, should precisely tally
with the nodes of the two sets of refractive indices.
To exhibit this fourth law, it is needful to determine the nodes
of the wave-lengths and the nodes of the refractive indices. To
find the nodes of the wave-lengths in a regular medium : Let
Cx be the extrusion of c, and d^, the extrusion of d, then
whence n^ is easily found. So from
n^ may also be easily found. Then
c^ + 4: c.,, : : C — D : C — N^
gives N„ and
gives Ng; whence should arise--— a = Wi and -^—a = nc^', also
N — N ^ ^
—J '^ = riy — Wg. The nodes having been calculated an d checked
by these formulae, the refractive indices of the nodes result from
— i='^N. and^^'^N,.
Wj ng
The nodes of the refractive indices Vj, Vg will be found by a
similar process. Here '*C— '"-C corresponds to c,,., and '"'D— '"D
of Chromatic Dispersion. 171
corresponds to <f, ; whence we have
(MC -'^•^C) + C^-^D -'^D) : f C -'^^C) : : '^D -'^C : '^C + v„
whence Vj may be found ; so also
(M2ji_fxp^ ^ C^G-'^^G) : '^^F-'^F : : '^G-'^F : '"F + Vg,
whence v^ may be found. Thence should arise respectively
'*Ni = Vi and '*N2=j/2 j that is, the refraction of the node should
be the same as the corresponding node of the refractions.
When the corrections on the refractive indices, and the corre-
sponding extrusions required by these laws, shall have been
made where necessary, there will be obtained a series of values
of these two sets of quantities perfectly self-harmonious, all the
errors arising from inaccuracy of observation having been made
to neutralize each other. The resulting figures will be found to
agree so nearly with those obtained from observation, as to leave
not a doubt of the real existence of the several laws which have
been thus ascertained, and of the accuracy of the method of in-
vestigation pursued.
So much for the regular media, which all present the foregoing
characteristics; and now for the peculiar. The only media yet
ascertained to fall under this class are the following eight : —
Alcohol.
Oil of cassia.
Oil of anise, T. 15°.
Muriate of zinc.
Pyroligneous acid.
i\Iuriatic acid.
Solution of soda-
Sulphuric acid.
The peculiarities presented by these media, as respects their
extrusive property, are of three kinds : — 1st, an alteration in the
position of the nodes ; 2nd, an alteration in the character of the
transfer of motive energy ; and 3rd, an alteration in the number
of the nodes, involving, as a consequence, both the other two
peculiarities.
Alcohol has its upper node between B and C, its lower between
F and G ; it may therefore be termed high nodal. Oil of cassia
has its upper node in the usual place between C and D, but its
lower between G and II ; it may therefore be termed low nodal.
Oil of anise, at temp. 15°, is also low nodal; but at the other two
temperatures examined it is regular. The muriate of zinc pre-
sents two peculiarities. It is, like alcohol, high nodal ; but it is
also medio-negative ; that is, the transference of motive energy is
from the central to the terminal parts of the spectrum, being
the reverse of what is observed in regular media. Its nodes are
between B and C and E and F, near F.
The remaining four ])resent more than two nodes, thus invol-
ving an oscillation of the transfer of motive energy. Pyrolig-
neous acid has three nodes — between B and C, C and D, G and
172 Mr. M. Ponton on certain Laws
H near G, so that the tirst is the abnormal node. The transfer
of energy takes place from C and H to B, D, E^ F, and G.
Muriatic acid has four nodes — between B and C, C and D,
D and E, F and G, the transfer of energy being from B, D, G, H
to C, E, F.
Solution of soda presents also four nodes — between B and C,
C and J), E and F, G and H. The transfer of energy is from
B D E H to C F G.
Sulphuric acid has no less than five nodes — between B and C^
D and E, E and F, F and G, G and H. The transfer of energy
is from BEG to C D F H. This medium has the smallest
amount of extrusive power of any yet examined.
It would be well to have the observations on these eight media
carefully repeated, in order to ascertain how far these peculiari-
ties, or any of them, may be due to serious errors of observation, —
a supposition which will in the sequel be shown to be very highly
probable. At the same time it would be difficult to assign any
reason why such peculiai'ities should not exist, or why all media
whatever should conform to one uniform type.
Meanwhile, assuming the observations to be nearly correct, it
is needful to point out the changes which these several peculiari-
ties introduce into the laws before indicated.
1st. The law of equal transference subsists unaltered.
2nd. The semel-bis-ter law undergoes the following modifi-
cations. The regular type being
36, + 2c,-4=3A. + 2y,,-/,,
it becomes in high nodal media,
3Z/--2c;.-^, = 3A,+ 2^,-/,;
in low nodal media,
3i^, + 2c^—cI^ = Bh^—2ff^—f^ ;
in pyrohgneous acid,
-3b- + 2c,-d,=zSK-2ff,-f,;
in muriatic acid,
Sb,- 2c, + 4 = 3/i. + 2^,-/, ;
in solution of soda,
3b,-2cr + d,=SK-2(/,-f,i
in sulphuric acid,
3b,-2c,-d,= -SK + 2ff,-f,.
Hence the general expression for this law must be
±Sb,±2c,±d,= ± M, ± 2g, ±f,.
3rd. As respects the law of the cquicentral common difference,
one general rule will suffice. Where the pairs b^ and h^, c,r and
of Chromatic Dispersion. 1 73
ffx, djc and/r have like signs, as in regular media, ihexx: differences
are to be taken to form the three quantities h^, S^, 8^, whose
three differences form the required progression. But if the
members of any of the above pairs have unlike signs, then their
sum is to be taken instead of their difference. Thus if h., and
hx stand on opposite sides of the account, we must take the sum
instead of the difference of this pair to constitute the quantity Sj ;
and so with the others.
4th. The law of coincident nodes is not aflfected by these pe-
culiarities,— the indices of the nodes, and the nodes of the indices
always coinciding very nearly, whatever may be the position or
number of the nodes.
With respect to the general formula for expressing the extru-
■yr
sivc power of a medium, namely o + Q + 2X = 0, the con-
stitution of the quantities K and Q is materially modified by
these peculiarities. As a general rule, all the fixed lines which
undergo positive extrusion are to be added together in one sum,
and all those negatively extruded into anothei', and the difference
between those two sums will be K. Thus in hiffh nodal media
we have
(C+D + E + F)-(B+G + H) = K2;
and in low nodal,
(D + E + F + G)-(B + C + H) = K33
and so with the others.
In like manner, those of the quantities h, c, d, &c., w'hich are
positively extruded, are to be collected into one sum, and those
negatively extruded into another, and the difference between
those two sums will be Q.
Thus in high nodal media we shall have
(c + r/+ e +/) - (i +i/ + A)= Q2 ;
in low nodal,
(r/ + ^+/+/7)-(6 + c + /0 = Q3.
The alterations introduced by an increase in the number of the
nodes will be easily understood from the above.
The calculations from which the foregoing laws have been de-
duced have been based on the relative normal wave-lengths for
the fixed lines, assuming that of B as unity, according to the
values given in the separate paper on that subject*. These values,
with their logarithms, stand as under : —
B. C. D. E. F. G. H.
1000000, 0-953893, 0-8560.")9, 0764567, 0704210, 0-623398, 0-570655,
00000000, 1-9794999, 1-9325036, 1-8834154, 1-8477024, 1-7947653, 17563732.
* This paper will be given in a subsequent Number. — Ed.
174 Mr. M. Ponton on certain Laws
From a considerable number of trials made with various sets
of normals, it appears that any alteration on the above numbers,
within the probable limits of error, would not affect the general
character of the laws above indicated.
From the foregoing investigation it follows that the refractive
index deduced from observation for any of the fixed lines, is a
somewhat complex quantity. In the first place, each index in-
volves a certain fixed amount e, which is constant for waves of
every length. It is the common divisor by which the differences
between the normal wave-lengths would have to be divided, in
order to produce within the medium a set of wave-lengths which
should present no extrusion of the fixed lines, but in which each
line should occupy the same position in relation to the others as
the normal lines occupy iu the spectrum produced by transmit-
ting a divergent beam through a system of equidistant fine lines.
This quantity e is always less than the observed refractive index ;
so that it forms only a portion, yet by much the greater propor-
tion of its amount. Had all the fixed lines this constant e as
their common refractive index, the medium would then have
refractive power without either dispersive or extrusive power.
Although no single medium exhibits this peculiarity, it is pos-
sible by a combination of two or more substances to obtain a
compound medium that shall present this condition, which is
that of achromatic refraction. The preceding investigation, if
followed out, may tend to facilitate the effecting of such com-
binations.
As the purely refractive power of a medium is due simply to
the state of compression of the aether within its pores, the con-
stant € may be viewed as the measure of that compression, and
may accordingly be termed the compressive index of the medium,
as distinct from the refractive index, which is a complex quan-
tity ; or it might be termed the optical elasticity of the medium,
for it is at least a measure of that elasticity. In doubly-refract-
ing media the value of e differs considerably in the direction of
the different optic axes of the same medium, thus showing the
compressive power of the constituent molecules to be specific and
polarized.
The variety in the refractive indices of the fixed lines in any
medium is due primarily to its dispersive power. The effects of
this property, viewed apart from the extrusive power, are exhi-
bited by the series of indices '^B, ''^C, &c. obtained from the
formulae a = u^ and —=tic,, in which only the normals and
e Vc>
the two constants e and a are involved. The differences between
this series of indices and the constant e may accordingly be
viewed as the respective dispersive indices of the fixed lines in
of Chromatic Dispersio n. 175
the particular medium. The constant a maybe termed "the
optical abstract/^ because it must be taken from the normal
wave-length corresponding to each of the fixed lines after it has
been divided by the constant e, in order to obtain the internal
wave-lengths b^, Co, &c.
The quantity a is thus indicated as being a portion of the
refracted wave-lengths, distinguishable from the main body, and
of the same magnitude for all waves. But while it is thus con-
stant for the same medium and temperature, yet in comparing
one medium with another, the value of a will depend on the con-
stant e, and on s the sum of the internal wave-lengths jointly ;
for S being the sum of the normal wave-lengths, the value of a
S
s
is = — - — . The constants e and a are thus mutually indepen-
dent, inasmuch as a may be indefinitely altered without aff'ecting
e, and vice versa.
The product of these two constants, or ea, deducted from each
of the normal wave-lengths, will show the extent to which each
normal is shortened during its passage through the medium, in
virtue of the dispersive power alone. The actual loss of length
being represented by ae, is of the same magnitude for all waves ;
but it of course tells more on those waves which are primarily
shorter. Hence the cumbers representing the loss of length
sustained by each wave in proportion to its primary length, from
the operation of the dispersive power of the medium alone, irre-
spective of either its refractive or extrusive powers, are in exact
inverse proportion to the primary wave-lengths.
Thus, taking as an example the bisulphuret of carbon (a
medium of high dispersive power), its constant a is 0"038772,
and ea = 0"058953, which, being deducted from each normal
wave-length, gives as under :
BIOOOOOO C0953893 DO-856059 E0764567 FO-704210 G0C23398 HO-570655
0-058953 0058953 0058953 0-058953 0-058953 0058953 0058953
¥941047 0^4940 0-797106 0705614 0-645257 0-564445 0-511702
Dividing these remainders by the normal wave-lengths, we obtain
B 0-941047, CO-938197, D 0-931135, E 0-922894, FO-916285, G 0-905433,
11 0-896693,
which numbers represent the reduced wave-lengths, reckoning
each wave as unity ; consequently the complements of these
numbers, being
BO-058953, CO-061803, D 0068865, EO-077106, FO-083715, G0-0945C7,
110103307,
represent the loss of length sustained by each wave, in propor-
176 Mr. M. Ponton on certain Laws
tion to its primary length, from the operation of the dispersive
power of the medium alune ; and these are in inverse proportion
to the primary wave-lengths. Thus also the proportion of the
refractive indices corresponding to this temporary loss of wave-
length, must also have a certain dependence on the initial force
which generated the particular wave to which the index belongs,
and may be found by multiplying the indices ^Bg, ^Cg, &c. (being
the observed indices freed from the portion due to the extrusion)
by the above complementary numbers, representing the loss of
length sustained by the waves from the operation of the disper-
sive power. Thus, in the case of the bisulphuret of carbon, the
indices '^Bg, '^Cg, &c. are
f^B^ 1-615760, /^Ca 1-620667, '^Do 1-632958, /^Ej 1-647542, '^Fg 1-659425,
MGj 1-679311, '^112 1-695681.
These, multiplied by the above series of complementary numbers,
give for the proportion of the indices due to the dispersive power,
B0095255, CO-100162, D0112453, EO-127037, FO-138920, GO-158806,
HOI 75176,
which numbers are identical with the differences between the
above indices and the constant e= 1-520505.
In different media, the loss of length sustained by any one
wave through the action of the dispersive power is always pro-
portional to the constant a, which may be accordingly regarded
as a measure of that loss.
To generalization beyond this point, the uncompensated errors
of observation and the yet unascertained effects of change of tem-
perature are a serious obstacle. But the data already obtained
may be found useful in detecting some of those errors and effects,
and in determining their probable limits.
As regards the effects of temperature, the most instructive
cases are those of the oils of cassia and anise ; for of these we
have observations at three different temperatures, though unfor-
tunately these do not coincide in the two media. Comparing
the values of e in these two fluids for the three sets of observa-
tions, they will be found as under : —
Oil of Cassia. Diff. Oil of Anise. Diff.
No. l.Temp. 10' e = 1-477740 . 2478
2. „ 14" 1-475262 . 5726
3. .. 22-5 1-469536 . 8204
No. 1. Temp. )3°-26 = 1-478492 . 989
2. „ 15°1 1-477503 . 4044
3, „ 20°-9 1-473459 . 5033
It will be perceived that not only are these values of e in the
inverse order of the temperatures, but that their differences are
not far from being proportional to the differences of temperature.
To make them exactly so, they would have to be altered thus : —
of Chromatic Dispersion. 177
Oil of Cassia. Diff. Oil of Anise. Diff.
No. 1. 6=1-477811 . . 2621
2. 1-475190 . . 556!)
3. 1-469621 . , 8190
No. 1. 6 = 1-478606 . . 1217
2. 1-477389 . . 3813
3. 1-473576 . . 5030
The above correction may be effected by an alteration of the
indices so' small as to be of no account.
This law, then^ that the indices of elasticity of the sether in
the pores of any medium are in the inverse order of the tempe-
ratures, and the differences of the indices are proportional to the
differences of temperature, may be regarded as rendered highly
probable by these two cases, being the only media on which we
have observations at more than two temperatures, so as to illus-
trate this point.
The subsistence of this law in the case of oil of anise is all the
more remarkable, because the indices of all the fixed lines are there
greater in No. 2 (the intermediate temperature) than in either
No. 1 or No. 3, thus showing the absolute magnitudes of these
indices alone to be an imperfect criterion by which to judge of
the condition of the sether within the pores of the medium. This
law thus removes an anomaly which would otherwise be presented
by the oil of anise, in which, were we to judge by the indices of
the fixed lines alone, we should be led to infer that, in passing
from temperature 13'^'25 to temp. 15°'l, the enlargement of the
pores is attended by an increase in the tension of the rether, — a
result in the highest degree improbable. The foregoing investi-
gation shows that this is not the case, but that the tension of
the aether, as determined by the value of e, does actually dimi-
nish with the enlai'geraent of the pores, consequent on the rise
of temperature.
This law is important in reference to the undulatory theory,
being exactly what it would lead us to expect ; and it confirms
the conclusion that the quantity e is the true index of the elas-
ticity of the aether within the pores of the medium.
On comparing together the two media — the oils of cassia and
anise — it will be perceived that in the former the rise of 12°*5 of
temperature, from temp. 10° to temp. 22°-5, gives on the value
of e a decrease of 0008 190 ; and in oil of anise, the rise of 7°-65
from temp. 13°-25 to 20 '9 gives on e a decrease of 0-005030.
These two are so nearly proportional to each other, as to lead
to the inference that in two different media, in which the elas-
ticity of the rether is nearly the same, the effects produced by
a given change of tcmjicrature are also nearly the same.
From the foregoing, it appears that the effects of temperature
in altering the action of any medium on tlie light passing through
it are so considerable, as to render it highly desirable that obser-
vations should be made on each medium at six or seven different
178 Mr. M. Ponton on certain Laws
temperatures, in order that these might operate as a check on
each other.
It will be particularly noted that in each medium the con-
stants e and a are independent of the absolute magnitudes of the
extrusions, and are affected only by the relations v^hich these in-
dividually bear to each other. Hence, provided those relations
be preserved, the constants e and a will remain unaffected by any
alteration in the absolute magnitudes of the extrusions, which
may accordingly be multiplied by any multiple m, integral or
fractional, without altering e or a. These two quantities are
thus consistent with an indefinite number of sets of indices of
refraction, so that these last may always be altered in a certain
manner without affecting those constants.
This point being kept in view, the following general formula
will be found applicable to all media whatever, namely,
r B C D E
e«1 7t3 ITT— + 7r\ TT" + TTT ^H— +
(B-e^>)±?; {G-ec)±7] {D-ed)±'q (E-ee)±?;
F G
{'^-ef)±V^W^)±V ' (H-
the quantities ea and t] being each constant for the same medium
and temperature, and S being the sum of the normal wave-
lengths, or the total amount of vis viva involved, the conserva-
tion of which thus depends on these three constants. To find
T) p
the constant t), if we call the sum of the series r-r + ^
^ ii — eoKj — ec
4- &c. = 2, and call ^ = ea', then 97 is the difference between ea
and ea'. If « > a', then the sign of 17 is + ; if a' > a, the sign
of 77 is — , and in either case is constant for the medium and
temperature.
Now the value of 97 depends on the relation of X (the sum of
the positive or negative extrusions) to a ; and there may always
be found for each medium and temperature such a positive value
of X as shall make 77 = 0. This it is proposed to call the limitiyiff
value of X, and to denote it by X'. In some media this limiting
value nearly coincides with the actual value of X, as given by
observation ; in others the actual value is several times greater
than the limit ; while in a few it falls somewhat below it. Call-
X'
ing — =&), it will be found that, making a small allowance for
the effects of errors of observation, this quantity 00 is constant
for all media whatever ; so that in every instance we have aaj = X',
the limiting value of the extrusions. This constant « may be
of Chromatic Dispersion. 1 79
found from the following formula,
4(B + C + G + H)-3(D + E + r)
-g— — — =0,,
and its logarithm is 3-4216417.
With a view to a further generalization, it is needful to ex-
amine the effects produced on the extrusions by raising the
normal wave-lengths of the fixed lines to different powers, and
dividing these by the indices of refraction. Selecting for this
purpose the medium flint-glass No. 30 of Fraunhofer, the ob-
sened indices of which are pretty nearly accurate, it will be
found that, while with the first powers of the normals the extru-
sions are
B -0-000419, C -0-000159, D +0000277, E +0000468, F +0-000422,
G -0-000047, H -0-000542, S +0001167,
with the squares of the normals they are
B -0-000049, C -0-000025, D+0'000031, E +0-0000G3, F +0000068,
G -0-000026, H -0-000062, S +0-000162,
and with tlie cubes they become
B +0-000184, C +0-000027, D -0000148, E -0000159, F -0000096,
G +0-000020, H +0-000172, S +0000403.
It will be observed that in this last series the extrusions have
changed their signs, and are greater in amount than with the
squares. There must accordingly be an intermediate exponent
of the normals between 2 and 3, at which the extrusions will be
reduced to their lowest amount. This exponent of least extra-
sion will be found to be, for flint-glass No. 30, as nearly as pos-
sible 2 "2, with which the extrusions become
B +0-000007, C -0-000009, D -0000010, E +0-000004, F +0000024,
G -0 000017, H +0-000001, S +0-000036.
These values are so insignificant that they may be regarded as
arising from small errors of observation, and they may be entirely
thrown out of view in the calculation of the indices. The follow-
ing are the diftereuces between the indices thus calculated and
those given by observation : —
B -0-000020, C -0-000026, U -0-000038, E +0-000035, F +0-000138,
G -0-000130, II +0-000007.
These differences are so small as to lie quite within the limits of
probable error in the observed indices.
Now what is thus true of flint-glass No. 30, will be found to
hold good with respect to all other media. Each has a specific
exponent of least extrusion, which is constant for the medium
and temperature. The question thus arises, How is this expo-
180 I\Ir. yi. Ponton on Chromatic Dispersion.
nent of least extrusion to be determined ? On a careful analysis
of all the media, it will be discovered that the value of this ex-
ponent depends entirely on the proportion which the extrusive
property of the medium bears to its dispersive power at a given
temperature; in other words, it depends on the proportion
which the irrationality bears to the length of the spectrum, with
a given prism and at a given distance from the prism. Repre-
senting the dispersive power by the o])tical abstract a, and the
irrationality by the amount of the positive and negative extru-
2X
sions 2X, and calling — ^ = pthe ratio which the extrusion bears
to the dispersion — representing also the exponent of least extru-
sion by n, we have the following equation universally applicable,
- ., = constant.
n— 1
The value of this constant, as determined from the best of the
observations, appears to be as nearly as possible 0'0092593*;
at least this value is sufficiently near the truth for all practical
purposes. The reciprocal of this number is 10"8, which, added
to unity, gives 11*8 as the highest limit of these exponents, or
that which the medium would have if p were = 1, or 2X=o.
The lower limit of these exponents, being 1, obtains when a is
equal to the above constant, or a = 0'009259 and 2X = 0.
As p is obtainable with tolerable correctness from any set of ob-
servations ivhich are approximately accurate, the exponent of least
extrusion may always be found from the equation 10'8p-f 1 = /?,
for any medium and temperature. It is unnecessary, in estima-
ting these exponents, to go beyond the first place of decimals,
which gives their value sufficiently near for the purposes of cal-
culation.
The exponents calculated from this equation for the various
media will be found specified in Table I. From this specifica-
tion the muriate of zinc is excluded, because it forms an excep-
tion. This circumstance, however, need not lessen confidence
in the correctness of the law ; for it only tends to confirm the
opinion expressed by the observer himself, that the indices which
lie has given for this medium are so inaccurate, that no conclu-
sion can be formed with respect to it till further observations be
made.
The exponents of least extrusion having been thus ascertained
from the observed indices of refraction, the next step is, by means
of the exponent, so to correct the indices as to reduce the extru-
sions to zero — a matter of easy accomplishment ; for the extru-
sions being thus eliminated from the calculation, the formula
* This value is of course open to future correction.
Method of estimating Phosphoric Acid and its Compounds. 181
for expressing the relation of the primary wave-length of any of
the fixed lines to its index of refract on, becomes universal and
quite simple. Denoting the wave-length by \, and the corre-
sponding index of refraction by fi, we have in every case
• f'^x^ ^
On
where the exponent n is constant for the medium and tempera-
ture, as are also the quantities e„ and a^,, being the index of
elasticity and the optical abstract corresponding to that expo-
nent. These two are ascertainable from the observed indices, in
the same manner as are e and a for the first power of the nor-
mals, and they will be found specified for each medium in
Table I.
The indices of refraction for the various media, as calculated
from this general formula, are given in Table VI., while the
observed indices are specified in Table VII. The differences
between the calculated and observed indices are exhibited in
Table VIII.
[T© be continued.]
XXIII. On a Simple and Ea^pedifious Method of estimating Phos-
phoric Acid and its Compounds, which is particularly applicable
to the Analysis of Phosphatic Manures and the Ashes of Plants.
By Edmund W. Davy, M.B., M.R.I.A. 6;c., Professor of
Agriculture and Agricultural Chemistry to the Royal Dublin
Society^.
THE want of some simple and expeditious method of esti-
mating phosphoric acid and its compounds has long been
felt ; for though several means have been devised for the deter-
mination of this acid under different circumstances, they arc so
complicated and require so much time in their performance, that
they are quite unsuited for many cases where expedition is
particularly required.
After much investigation I have succeeded in devising a
method which is very quickly performed, easy of execution, and
capable of affording extremely accurate results. It is founded
on the fact that phosphoric acid possesses a great attraction for
the peroxide of iron, so that when a persalt of that metal is
added to a solution containing phosphoric acid, an insoluble
combination of the peroxide of iron with that acid is produced,
which under particular circumstances has the following com-
* Communicated by the Autlior, being part of a paper read before the
Royal Dublin Soeietv, January 11, 1860.
'Phil. Mag. S. 4 Vol. 19. No. 126. March 1860. O
182 Prof. Davy on a Simple and Expeditious Method of
position, viz. (Fe^ 0^, PO'^), in which 80 parts of the peroxide
containing 56 of metallic iron, are combined with 72 parts of
phosphoric acid.
The fact of the peroxide of iron forming an insoluble com-
pound with phosphoric acid has long been known ; and different
methods founded on it have been proposed and adopted for the
estimation of phosphoric acid and its compounds, — as, for ex-
ample, those of Berthiei", Kobell, and Raewsky, which are described
in different works on analytical chemistry.
Each of those methods, however, requires a considerable
devotion of time, from the collecting, washing, drying, igniting,
weighing, and other operations through which the precipitated
phosphate of iron has to pass, which not only consume much
time, but, unless they are very carefully performed, lead to great
inaccuracies in the results obtained.
In the modification I propose, I dispense altogether with those
tedious and troublesome operations, by simply adding a gra-
duated solution of iron of known strength to the phosphate, and
ascertaining the point when sufficient iron has been added to
combine with all the phosphoric acid present ; and from the
quantity of iron employed, I calculate the amount of that acid ;
every 56 parts of iron being equivalent to 72 of phosphoric
acid.
The iron solution which I use for this purpose is somewhat
different from that hitherto employed. I make it in the follo\\ing
manner : a certain quantity of the finest pianoforte iron wire,
perfectly clean and free from rust, is dissolved in pure hydro-
chloric acid, and sufficient nitric acid is afterwards added to
convert the so-formed protochloride into the perchloride of iron ;
and as any excess of hydrochloric acid would be injurious to the
process, and as it cannot be removed by heating the mixture and
evaporating it to dryness, which would decompose a portion of
the perchloride, giving I'ise to peroxide of iron and hydrochloric
acid, I add caustic ammonia till all the free acid has combined
with that substance, and a small quantity of the peroxide of iron
precipitated by the alkali remains undissolved after agitating the
mixture and allowing it to stand for a few minutes. Acetic acid
is then added to dissolve the oxide, and when it has effected its
complete solution (which it will do by leaving the acid to act on
the oxide at the ordinary temperature for a short time), the mix-
ture is largely diluted with distilled water and graduated in the
usual way, so that the amount of iron may be known which is
contained in a given quantity of the liquid. The proportions
which 1 have used are 100 grains of iron in 1000 cubic centi-
metres of the liquid ; and this quantity of standard solution will
suffice for a great number of determinations.
estimating Phosphoric Acid and its Compounds. 183
This liquid, which contains the perchloride and peracetate of
iron, together with the chloride of ammonium, the acetate of
ammonia, and a little free acetic acid, I find to be well adapted
for the estimation of phosphoric acid ; and as it appears from my
experiments that it may be kept for a considerable time without
undergoing any change, it is therefore preferable to the acetate
and other salts of iron hitherto employed, which, from their
proneness to decompose, require to be freshly prepared before
using them. Having made the standard solution of iron, the
next step is to prepare the phosphate, and if it is (as is ge-
nerally the case) an insoluble one dissolved by an acid, am-
monia is tii'st added to the solution till it is distinctly alkaline
to turmeric paper*, then acetic acid to redissolve completely
the phosphate precipitated by the ammonia, and leave that acid
in slight excess ; and finally the standard solution of iron is
carefully added from a Mohr's alkalimeter, or any other con-
venient form of volumetric apparatus f, till the ii'on begins to be
in slight excess.
I ascertain this point by taking out of the mixture (after it
has remained a few minutes with occasional stirring to effect the
complete combination of the oxide of iron with the phosphoric
acid) a drop of the solution on the end of a glass rod, and
touching with it a piece of thick and close-textured filtering
paper, under which is placed some ordinary filtering paper,
which has been previously saturated with a strong solution of
gallic acid, and then dried.
By this arrangement we avoid filtering : the insoluble phoa-
phate of iron formed in the process being retained by the upper
paper, and the solution passing down to the lower, at once shows,
by the light-purplish stain produced, the point Avhen sufficient
iron has been added to combine with all the phosphoric acid
present, and a very minute excess exists in the mixture J.
This experiment being repeated a second or third time, by
having the phosphate under examination dissolved in a given
quantity of solution and taking a certain amount of it for each
* A large excess of ammonia should be avoided, for by its afterwards
combining with the acetic acid to form the acetate of ammonia, which dis-
solves to a slight extent the phosphate of iron, the amount of phosphoric
acid estimated in that case by this process is somewhat diminished. A
large excess of acetic acid, however, appears to affect but very slightly the
results obtained.
t The form which I have used and found most convenient is Mohr's
alkalimeter with the addition of Professor Erdmanu's iloat, which affords
great facilities for the accurate reading of tlie volume of liquid employed.
+ When the excess of iron added is very minute, I have found that by
gently drying the wet spot on the galhc acid paper, the stain becomes
more visible.
02
184 Prof. Davy on a Simple and Expeditious "Method of
determination, we ascertain tlic exact quantity of iron solution^
and therefore of iron, necessary to produce this eflfect ; and from
this we easily calculate the amount of phosphoric acid present
in the manner before explained.
Though the ferrocyanide and the sulphocyanide of potassium
may be substituted for the gallic acid, using them in the way
I have described for that acid, still I have found gallic acid to
give more satisfactory results than either of them, and to be an
exceedingly sensitive test to the presence of iron in solution.
For I found, by direct experiment with 2 cubic centimetres of
the iron solution containing 0"2 parts of a grain of iron, diluted
with distilled water so as to make up 300 cubic centimetres, that
one drop of this mixture let fall on the gallic acid paper, produced
a faint purplish stain, and the smallest drop which could be
taken up on the top of a glass rod gave with a solution of gallic
acid a very decided effect ; so that this test is one of great deli-
cacy in ascertaining the point when the slightest excess of iron
has been added to the mixture in this method for the estimation
of phosphoric acid and the phosphates. I may observe that
when the phosphate under examination is very largely diluted
with water, it will lead to more accurate results to reduce by
evaporation the bulk of the liquid (having previously added a
little hydrochloric acid in those cases where evaporation would
cause the precipitation of any insoluble phosphates), — the eflfect
of large dilution, by its rendering the gallic acid less sensitive to
the point when iron is in excess, being to indicate a somewhat
greater amount of phosphoric acid than is present.
This source of inaccuracy might also in a great measure be
obviated by seeing how much of the iron solution was necessary
to give an indication of that metal when it was diluted with a
bulk of fluid equal to that employed in the experiment; and
this being deducted from the quantity of iron necessary in the
determination, would give a very close approximation to the real
amount required to combine with the phosphoric acid, where it
might be inconvenient and occupy too much time to evaporate
the liquid.
Hitherto the estimation of phosphoric acid volumetrically by
the use of a standard solution of iron has been thought by many
to be impracticable, as the analyses of different chemists show that
the composition of phosphate of iron is subject to great variation.
This, however, may be accounted for by the different circum-
stances under which it has been formed by those experimenters,
which give rise to phosphates of diflferent constitution. But I
entertain no doubt that, by always placing the oxide of iron and
the phosphoric acid under the same conditions, compounds of
the same constitution would in every case be formed.
estimatinrj Phosphoric Acid and its Compounds. 185
Be this as it may, my experiments have clearly shown me that
under the conditions in which T place those substances, in the
method recommended for the estimation of phosphoric acid, a
compound having the composition (Fe^ 0'^, PO^) is uniformly
produced. I have proved this by taking certain quantities of
different phosphates and treating them in the manner described,
I ascertained how much iron was necessary to combine with the
phosphoric acid present ; and in every case I have obtained re-
sults which agree almost exactly with those I should have got,
calculating according to that formula, which would not have
been the case had the composition of the phosphate of iron been
different.
The following are taken from among my experiments. Some
pyrophosphate of magnesia and tribasic phosphate of lime being
carefully prepared, a certain quantity of each was taken and dis-
solved by the aid of heat in a little hydrochloric acid ; and the
solutions being diluted with distilled water, they were very care-
fully graduated, so that 5 cubic centimetres should contain one
grain of each of those compounds.
Common tribasic phosphate of soda was hkewise taken, and
after being exposed to a red heat for some time to convert it into
the anhydrous pyrophosphate, a solution of it was also made, con-
taining the same proportion of dry salt as in the former cases.
Five cubic centimetres of each solution (containing one grain
of those compounds) were then taken and several estimations
made, employing the same quantity of solution every time, when
the results obtained were as follows : —
Amount of iron required to combine with the phosphoric acid
contained in one grain of —
By Calculation, By Experiment,
parts of a grain, parts of a grain.
0-5000 1st Experiment 0-5000
M 2nd „ 0-5000
Pyrophosphate of magnesia <
Tribasic phosphate of lime
„ 3rd „ 0-5000
. „ 4th „ 0-5000
'0-3589 1st „ 0-3G00
„ 2nd „ 0-3G00
3rd „ 0-3600
_ „ 4th „ 0-3600
rO-4179 1st „ 0-4200
Anhydrous pyrophosphate J „ 2nd „ 0-4200
of soda* ] „ 3rd „ 0-4200
L ,y 4th „ 0-4200
* In the case of the bibasic salts, it is necessary to convert them into the
tribasic before the addition of the iron solution ; this I have found (in the
186 Mr. J. Spiller on the Composition of
These results, agreeing so closely with those obtained by cal-
culation, prove that such a compound of the oxide of iron and
phosphoric acid was produced, otherwise the calculated amount
of iron would have been very different from that obtained by
experiment.
They also show how very accurate this method is, and how
constant are the results obtained by its adoption ; and the ease
and expedition with which the estimation of phosphoric acid
is eflfected, renders it a very useful means for the determination,
not only of that acid itself, but likewise for that of many of its
compounds, which can easily be calculated from the amount of
phosphoric acid present.
I have already found that it is particularly useful in estimating
the quantity of soluble and insoluble phosphates in superphos-
phate, a manure the analysis of which has hitherto been attended
with considerable trouble. And from my experiments I have no
doubt that it will be found to be extremely useful in the esti-
mation of the phosphates in dififerent manures, the ashes of
plants, and many other cases of common occurrence where an
expeditious determination of the quantity of those substances is
required.
Laboratory of the Royal Dublin Society,
February 3, 1860.
XXIV. On the Composition of the Photographic Image.
Bij John Spiller, F.C.S., of the War Department*.
THE composition and chemical nature of the photographic
image, as produced by the action of light upon the chlo-
ride of silver, is even at the present moment, notwithstanding
the numerous experiments recorded on the subject, one upon
which authorities are divided. While there is abundant evidence
to show that the darkening consequent on exposure to the sun's
rays is a process of reduction accompanied with the evolution of
chlorine, there are yet two opinions entertained as to the extent
to which this reducing action ordinarily proceeds. In accordance
with one hypothesis, the white or protochloride of silver (Ag CI)
is assumed to suffer the full decomposition into its elements,
two cases I have tried, viz. the magnesia and soda salts) to be easily
efiFected by heating them for a few miuutes with a little hydrochloric acid.
But in these as in other cases, the solution of the phosphate must be
suffered to cool to the ordinary temperature before the estimation of the
])hosphoric acid is attempted, as heat alters the conditions, and ajijiears to
give rise to a different compound of the oxide of iron and phosphoric acid.
* Communicated by the Author.
the Photographic Image, 187
becoming therefore reduced to the state of metal ; while according
to a second view, the progress of this reducing action is limited
to an intermediate stage, whereby a compound is produced con-
taining less chlorine by one-half than the original substance,
and to which the name and formula, subchloride of silver
(Ag^ CI), have been applied. As a contribution towards a fuller
explanation of the chemical changes involved, I beg to submit
the following results of a series of experiments, made at inter-
vals of leisure during the summers of 1857, 1858, and 1859,
which would appear strongly to favour the first-mentioned hy-
pothesis.
Preliminary experiments upon the freshly precipitated chlo-
ride of silver, as ordinarily prepared, having demonstrated the
difficulty of eflPecting more than a mere superficial decomposition
by exposure to sunlight, a process of preparation was adopted
whereby an exceedingly finely divided condition of the substance
was ensured, and its exposure conducted under circumstances
favourable to its thorough decomposition. For this purpose
highly dilute solutions were prepared, both of nitrate of silver
and chloride of sodium, in proportions so adjusted that equal
bulks represented amounts of chlorine and of silver in the ratio
of their chemical equivalents.
(5"85 grains of pure rock-salt, on the one hand, and 17 grains
of fused and neutral nitrate of silver, were dissolved each in
two gallons of pure distilled water.)
When equal measures of these solutions were mixed in an
obscurely illuminated apartment, the white chloride of silver
was precipitated in a form so finely divided that an opalescence
only, without visible particles, was at first apparent. By dif-
fused daylight this became quickly darkened, and in the course
of time subsided into a very small purple-grey deposit. But in
order to ensure full decomposition, it was the general practice to
employ the silver solution in excess and to add the salt water
under the full action of sunshine, the liquid being contained in
three, and sometimes four, pale glass flasks, each of nearly two
gallons capacity, which were placed on the roof of one of the
buildings in the Royal Arsenal, Woolwich, and in such a posi-
tion that the solar rays had uninterrupted access to their con-
tents, almost from sunrise to sunset. Under favourable circum-
stances it was then frequently impossible to observe the formation
of the white chloride of silver on mixing the two solutions, so
rapidly was it converted into the dark coloured product. At the
expiration of the day's action the small precipitate had become
completely darkened, and in the same time had subsided, so that
on the following morning the supernatant liquid could be drawn
off through a siphon, and a fresh charge introduced, the pro-
188 Mr. J. Spiller on the Composition of
duct being usually collected from the flasks at intervals of two
or three days.
In this manner, during the remarkably brilliant days in June
and July 1857, no less than forty-six gallons of the standard
solutions were submitted to treatment, and a comparatively con-
siderable quantity of the darkened material procured for in-
vestigation.
The appearances presented during these trials were often such
as to indicate a reduction more complete than that which would
probably be required on the subchloride hypothesis : — first, a
thin pellicle of high metallic lustre, white as silver, was usually
seen floating on the surface of the liquid, and the internal walls
of the flasks were frequently coated with a film much resembling
the condition of silver reduced by any of the so-called " silver-
ing" processes. The product also, although containing admixed
chloride, was susceptible of a high degree of lustre on being
burnished in an agate mortar.
In colour the products of several experiments varied a little, —
sometimes presenting a dark purple-grey appearance, at other
times the grev was slightly tinged with green ; and to this
depth of colour is probably attributable the circumstance that
sometimes, during exposure to the burning rays of a midsummer
sun, the contents of the flasks attained a degree of temperature
w^hich should be recorded as a condition of experiment, although
such heat may not be supposed to have exercised any special
influence in determining an abnormal decomposition. On the
24th of June, 1857, a hot sunny day with cloudless sky, the tem-
perature of the dark liquids in three of the flasks reached 110^,
115°, and IIG'^ Fahr. respectively; whilst at the same time,
3 P.M., a thermometer in the shade registered 83*^, and only 91°
with the sun shining freely on the mercury in the bulb j such
high degrees of temperature were, however, unusual and never
again observed.
With a view to counteract the possibility of the material
undergoing alteration by drying, it was constantly preserved
under water, and in the moist condition submitted to numerous
experiments for the purpose of ascertaining its constitution.
On determining by chemical analysis the composition of an
average product, it was found to contain a larger proportion of
silver than the original white chloride, as will appear in the
following comparison : —
Composition of Found in
white chloride. grev product.
Silver . . . 75-26 . . . . 'Sl-O
Chlorine. . . 24-74 .... 190
10000 100-0
the Photographic Image. 189
A substance having the composition specified in the second
column, cannot be referred to any probable formula, but would
appear to be composed of a mixture of silver with unaltered
chloride, in about the proportion that would result from the
destruction of two only in every seven parts of white chloride
submitted to the action of the sun^s rays. This, as already
stated, represents the extent of decomposition on the average
product ; but special experiments, in which the nitrate of silver
was employed in greater excess, and the chloride solution un-
usually dilute, enabled me to prepare, on the very brilliant day,
June 16th, 1857, a product containing more than 82 per cent,
of silver, and in which it might be assumed that one-third of the
total amount of white chloride operated upon had become re-
duced to the metallic state. In attempting to pass this stage,
the mechanical difficulty of tlie reduced silver particles encrusting
and offering protection to the undecomposed white chloride,
])resents an obstacle which only extreme dilution and excessively
tine state of division seem likely to combat.
In the application of the several chemical reagents by which
it was proposed to eliminate the portion of unaltered chloride in
admixture, and thus to isolate the essential matter which con-
stituted the darker residual portion, it was found impossible to
arrive at any other conclusion than that of its consisting of piu-e
silver : throughout the examination no evidence was presented
which pointed to the existence of the so-called subchloride of
silver, or at least of its production under these circumstances ;
but, on the contrary, it appeared to be uniformly proved that the
metal, somewhat modified in colour and physical condition by
the varying circumstances of the experiment, was in every case
the product resulting from the action of light upon the chloride
of silver.
The reactions more particularly examined were the following: —
Ammonia dissolved out from the substance the whole of the
unaltered chloride (afterwards recovered in a white scaly form
by the evaporation of the solvent), while it left insoluble a
grey residue of metallic silver in which no chlorine could be
found.
Cyanide of potassium solution dissolved away the chloride and
left metallic silver.
Hyposulphite of soda, employed in the form both of concen-
trated and dilute solutions, speedily dissolved out in the cold
the unchanged chloride, leaving a residue of grey metallic silver,
which contained neither oxygen, chlorine, nor sulphur.
Iodide of potassium operated first in the conversion of the
chloride into yellow iodide of silver, which, on adding an excess
of the reagent, was entirely taken into solution. The grey
190 Mr. J. Spiller on the Composition of
metallic residue, after repeatedly washing with dilute iodide of
potassium solution and finally with water, was found to consist
of silver without any admixture cither of chlorine or iodine.
Nitric acid in a cold and diluted form was inactive ; but more
concentrated acid effected the removal of the reduced silver by
converting it into nitrate (with evolution of red nitrous fumes),
and left insoluble the white chloride of silver j ammonia then
added dissolved completely this latter substance.
On the other hand, the darkened product was reconverted
into its original white condition, with varying degrees of rapidity,
by treatment with chlorine-water, nitro-hydrochloric acid, the
brown solution of bichloride of manganese, and by a mixture of
hydrochloric acid and chlorate of potassa. An acid solution of
the green chloride of copper had also the power of reconverting,
although more slowly, the darkened chloride into its primitive
condition ; and a similar change appeared to be brought about
by digesting in a cold saturated solution of chloride of mercury,
but in this instance the conversion was attended with a reduc-
tion of the mercury salt to the state of subchloride, so that a
black residue, derived from the calomel, remained on afterwards
attempting to dissolve the chloride of silver in ammonia.
It was in the next place thought desirable to prepare for com-
parison a sample of altered chloride which had not been so fully
acted upon by the light, and to restrict the excess of nitrate of
silver employed, in order to ascertain whether at an earlier stage
a more partial reduction, attended with the formation of an in-
ferior chloride, could possibly occur. On a cloudy day in Sep-
tember 1857, a purple product was obtained, which differed from
the former samples by containing a much larger proportion of
unchanged chloride ; and in consequence of the more marked
physical change- in the state of aggregation of the particles
attending the removal of this larger quantity of unaltered matter,
the colour of the substance exhibited a more striking transition
from purple to grey on treatment with hyposulphite of soda and
other solvents already enumerated. Neither in this instance was
any chlorine detected in the insoluble residual portion, nor evi-
dence furnished of its having been removed from a state of weak
chemical combination.
It will be perceived that the results now recorded bear refer-
ence to a series of experiments from which the interfering in-
fluences of organic matter, and all other chemical agents, ex-
cepting only water and the nitrates of silver and soda, have been
intentionally excluded. The motive for such a course rests on
the belief that the full and accurate determination of the action
of light in its simplest phase must precede other considerations
likely to involve secondary and more complex reactions, which
the Photographic Image. 191
will be better investigated after a full knowledge of the first has
been acquired.
The fact of clilorine being evolved during the decomposition
by solar agency of chloride of silver under water, has been repeat-
edly observed and is fully corroborated by my own experiments.
It follows, therefore, that if a solution of nitrate of silver be em-
ployed in conjunction with the chloride, as in the ordinary prac-
tice of photography, the evolved chlorine will exert its o^vn
peculiar action on the silver solution in contact, precipitating
from it an additional amount of white chloride, which in turn
becomes, partially at least, decomposed by light. It has been
assumed that the ivhole of the nascent chlorine is thus available
for the formation of new chloride of silver ; but this can, I think,
be true only if other matters are present having the power to
decompose hypochlorous acid, a product always formed to the
amount of half that of the available chlorine, according to the
reaction first pointed out by Balard,
C12 + AgO,NO^=AgCl + C10 + NO^
It might then be predicted that, by exposing pure white chlo-
ride of silver under a solution of the nitrate of known strength,
this latter would become continually weakened. This I find to
be the case; and in the event of employing a dilute solution,
every trace of silver is removed, leaving only mixed nitric and
hypochlorous acids as residual products dissolved in the water.
It is possible also to remove the metal from a solution of nitrate
of lead, by exposure to sunlight in contact with recently pre-
cipitated chloride of silver.
Again, inasmuch as the white chloride darkens with a rapidity
regulated by the energy with which the liberated chlorine is re-
moved from its sphere of influence, I have been able to prove*
that reducing agents, the protochloride of tin especially, as also
certain alkaline solutions, greatly facilitate the decomposition ;
while the higher chlorides of platinum and mercury are known
to exert a power in the opposite direction.
Several experiments were also made upon the chloride of silver
formed by the direct union of its elements — silver-leaf, electro-
plated daguerreotype tablets, and the silver specula obtained on
collodionized glass by the ordinary ])hotographic processes ;
these several conditions of silver, converted into chloride by the
action of chlorine gas, furnished products all of which suffered
decomposition on exposure to sunshine, but were very much less
speedily affected than the condition of precipitated chloride
* " On the alteration of Chloride of Silver by Light," Photographic
News, October 1859.
192 On the Composition of the Photographic Image,
usually employed in the practice of photography. The resulting
darkened surfaces were found to be capable of restoration by
renewed exposure to gaseous chlorine. These experiments were
pursued no further, as they did not appear to present so close a
parallel to the ordinary application of chloride of silver as the
system of preparation already described.
From a general examination of the products obtained by the
action of light upon several ef the more definite compounds of
silver, it appeared to me that the oxalate would be likely to pre-
sent the most indubitable evidence of reduction to the metallic
state, and from its ready decomposability be well fitted for com-
parison with the results aflForded by the examination of the
altered chloride. Some oxalate of silver was therefore prepared
by precipitation from nitrate of silver and oxalate of ammonia
(the formerln slight excess), washed by decantation, and exposed
under pure distilled water to the direct rays of the sun. The
white oxalate soon changed colour, becoming reddish brown,
and was seen to evolve small gas bubbles, which proved to be
carbonic acid by the water having now the property of precipi-
tating basic acetate of lead, producing a milkiness easily soluble
in acetic acid. That silver was, on the other hand, the product
of reduction, became evident on repeating the experiment with
a more finely divided condition of the substance, and by re-
moving the large proportion of unaltered material, which in this
instance also remained in admixture with the blackened parti-
cles. The same transition of colour from dark purple to grey,
attended the withdrawal of the undecomposed oxalate by dilute
hyposulphite of soda solution, and the metal was left in a state
of purity. Hence the decomposition will be expressed by
AgO,C2 03=Ag + 2C02.
Passing in review the results obtained in the foregoing expe-
riments, it will probably be considered that the weight of evi-
dence tends to show that the metal is the ordinary product of
the chemical action of light upon chloride of silver; and that
the principal difiiculty which has stood in the way of accepting
this conclusion has in a great measure to be accounted for by the
often varying shades of colour presented by the reduced metal,
and more especially the transition observed at the moment of
removing the unaltered portion of material by the application of
the fixing agent. If in these several stages the change m phy-
sical condition be considered in its proper connexion, and due
allowance be made for the very important influence known to be
exercised over the light-reflecting capacity of these minutely
divided particles by very slight modifications in their state of
aggregation (quite irrespective of change in chemical coustitu-
On the Simultaneous Emission and Absorption of Rays. 193
tion), there will then be no longer any difficulty in referring
these results, with others of the same class (e. (j. the several
varieties of gold prepared and examined by Professor Faraday*),
to a series all of which are capable of similar explanation.
I subjoin, in the form of propositions, a statement of the
results arrived at ; they appear to me to have been fully sub-
stantiated by the foregoing experimental considerations. And I
will remark, in conclusion, that the hypothesis believed to be
supported by the facts now communicated is in conformity with
the previous results of Dr. Guthrie, MM. Girard and Davanne,
and generally also with those of M. Van ]Monkhoven, and will
consequently be to a certain extent opposed to the views advanced
by Messrs. Hadow, Hardwich, Llewellyn, and Maskelyne, in
their joint report upon this subject recently presented to the
meeting of the British Association.
Propositions.
1st. That chloride of silver, when decomposed by light, is
separated into its elements,
2nd, That this change does not usually extend to the whole
bulk of the material operated upon, on account of the opacity of
the darkened ])roduct mechanically protecting a certain portion
of unaltered chloride of silver from the action of the light.
3rd. That the degree and rapidity of reduction is influenced
by the state of division of the particles, and by the presence of
agents capable of absorbing the chlorine when liberated from its
combination with silver.
Chemical Department, Royal Arsenal,
Woolwich, February 17, 18(i0.
XXV. On the Simultaneous Emission and Absorption of Rays of
the same definite Refrangibility ; being a translation of a portion
of a paper by M. Leon Foucault, and of a paper by Professor
KiRCHHOFF.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
SOME years ago ]\1, Foucault mentioned to me in conversa-
tion a most remarkable ph?cnomenon which he had observed
in the course of some researches on the voltaic arc, but which,
* Dr. Faraday showed that the red gold precipitated from solution by
phosphorus became violet merely by the addition of chloride of sodium.
(Notices of the Meetings of the Royal Institution, June 13, 1856,)
194 M. Foucault and Prof. Kirchhoff o« the Simultaneous
though published in Ulnstitut, does not seem to have attracted
the attention which it deserves. Having recently received from
Prof, KirchhoiT a copy of a very important communication to the
Academy of Sciences at Berlin, I take the liberty of sending you
translations of the two, which I doubt not will prove highly in-
teresting to many of your readers.
I am, Gentlemen,
Yours sincerely,
G. G. Stokes.
M. Foucault^s discovery is mentioned in the course of a paper
published in Ulnstitut of Feb. 7, 1849, having been brought
forward at a meeting of the Philomathic Society on the 20th of
January preceding. In describing the result of a prismatic
analysis of the voltaic arc formed between charcoal poles,
M. Foucault writes as follows (p. 45) : —
" Its spectrum is marked, as is known, in its whole extent by
a multitude of irregularly grouped luminous lines ; but among
these may be remarked a double line situated at the boundaiy
of the yellow and orange. As this double line recalled by its
form and situation the line D of the solar spectrurb, I wished to
try if it con-esponded to it ; and in default of instruments for
measuring the angles, I had recourse to a particular process.
" I caused an image of the sun, formed by a converging lens,
to fall on the arc itself, which allowed me to observe at the same
time the electric and the solar spectrum superposed ; I convinced
myself in this way that the double bright line of the arc coin-
cides exactly with the double dark line of the solar spectrum.
" This process of investigation furnished me matter for some
unexpected observations. It proved to me in the first instance
the extreme transparency of the arc, which occasions only a faint
shadow in the solar light. It showed me that this arc, placed in
the path of a beam of solar light, absorbs the rays D, so that the
above-mentioned line D of the solar light is considerably strength-
ened when the tw^o spectra are exactly superposed. When, on
the contrary, they jut out one beyond the other, the hne D
appears darker than usual in the solar light, and stands out bright
in the electric spectrum, which allows one easily to judge of theLr
perfect coincidence. Thus the arc presents us with a medium
which emits the rays D on its own account, and which at the
same time absorbs them when they come from another quarter.
" To make the experiment in a manner still more decisive, I
projected on the arc the reflected image of one of the charcoal
points, which, like all solid bodies in ignition, gives no lines ;
and under these circumstances the line D appeared to me as in
the solar spectrum."
Emission and Absorption of Rays of same Refrangihility . 195
Professor Kirchhoff's communication "On Fraunhofer's Lines,"
dated Heidelberg, 20th of October, 1859, was brought before the
Berlin Academy on the 27th of that month, and is printed in
the Monatsbericht, p. 662.
" On the occasion of an examination of the spectra of coloured
flames not yet published, conducted by Bunsen and myself in
common, by which it has become possible for us to recognize the
qualitative composition of complicated mixtures from the appear-
ance of the spectrum of their blowpipe-flame, I made some ob-
servations which disclose an unexpected explanation of the origin
of Fraunhofer's lines, and authorize conclusions therefrom re-
specting the material constitution of the atmosphere of the sun,
and perhaps also of the brighter fixed stars.
" Fraunhofer had remarked that in the spectrum of the flame
of a candle there appear two bright lines, which coincide with the
two dark lines D of the solar spectrum. The same bright lines
are obtained of gi'eater intensity from a flame into which some
common salt is put. I formed a solar spectrum by projection,
and allowed the solar rays concerned, before they fell on the slit,
to pass through a powerful salt-flame. If the sunlight were
sufficiently reduced, there appeared in place of the two dark
lines D two bright lines ; if, on the other hand, its intensity
surpassed a certain limit, the two dark lines D showed themselves
in much greater distinctness than without the employment of
the salt-flame.
" The spectrum of the Drummond light contains, as a general
rule, the two bright lines of sodium, if the luminous spot of the
cylinder of lime has not long been exposed to the white heat ;
if the cylinder remains unmoved these lines become weaker, and
finally vanish altogether. If they have vanished, or only faintly
appear, an alcohol flame into which salt has been put, and which
is placed between the cylinder of lime and the slit, causes two dark
lines of remarkable sharpness and fineness, which in that respect
agree with the lines D of the solar spectrum, to show themselves in
their stead Thus the lines D of the solar spectrum are artificially
evoked in a spectrum in which naturally they are not present.
" If chloride of lithium is brought into the flame of Bunsen's
gas-lamp, the spectrum of the flame shows a very bright sharply
defined line, which lies midway between Fraunhofer's lines B
and C. If, now, solar rays of moderate intensity are allowed to
fall through the flame on the slit, the line at the place pointed
out is seen bright on a darker ground ; but with greater strength
of sunlight there appears in its place a dark line, which has quite
the same character as Fraunhofer's lines. If the flame be taken
away, the line disappears, as far as I have been able to see, com-
pletely.
196 On thn Simultaneous Emission and Ahsoiytion of Rays.
" I conclude from these observations, that coloured flames in tiie
spectra of which bright sharp lines present themselves, so weaken
rays of the colour of these lines, when such rays pass through
the flames, that in place of the bright lines dark ones appear
as soon as there is brought behind the flame a source of light of
sufiicient intensity, in the spectrum of which these lines are
otherwise wanting. I conclude further, that the dark lines of
the solar spectrum which are not evoked by the atmosphere of the
earth, exist in consequence of the presence, in the incandescent
atmosphere of the sun, of those substances which in the spectrum
of a flame produce bright lines at the same place. We may
assume that the bright lines agreeing with D in the spectrum of
a flame always arise from sodium contained in it ; the dark line
D in the solar spectrum allows ns, therefore, to conclude that
there exists sodium in the sun's atmosphere. Brewster has
found bright lines in the spectrum of the flame of saltpeter at
the place of Fraunhofer's lines A, a, B ; these lines point to the
existence of potassium in the sun's atmosphere. From my ob-
servation, according to which no dark line in the solar spectrum
answers to the red line of lithium, it would follow with proba-
bility that in the atmosphere of the sun lithium is either absent,
or is present in comparatively small quantity.
"The examination of the spectra of coloured flames has
accordingly acquired a new and high interest; I will carry it
out in conjunction with Bunsen as far as our means allow. In
connexion therewith we will investigate the weakening of rays of
light in flames that has been established by my observations.
In the course of the experiments which have at present been insti-
tuted by us in this direction, a fact has already shown itself
which seems to us to be of great importance. The Druramond
light requires, in order that the lines D should come out in it
dark, a salt-flame of lower temperature. The flame of alcohol
containing water is fitted for this, but the flame of Bunsen's gas-
lamp is not. With the latter the smallest mixture of common
salt, as soon as it makes itself generally perceptible, causes the
bright lines of sodium to show themselves. We reserve to our-
selves to develope the consequences which may be connected with
this fact."
Note. — The remarkable phenomenon discovered by Foucault,
and rediscovered and extended by Ku-chhoff, that a body may be
at the same time a source of light giving out rays of a definite
refrangibility, and an absorbing medium extinguishing rays of
that same refrangibility which traverse it, seems readily to admit
of a dynamical illustration borrowed from sound.
On the Theory of Equations of the Fifth Degree. 197
We know that a stretched string which on being struck gives
out a certain note (suppose its fundamental note) is capable of
being thrown into the same state of vibration by aerial vibra-
tions corresponding to the same note. Suppose now a portion
of space to contain a great number of such stretched strings,
forming thus the analogue of a " medium.'^ It is evident that
such a medium on being agitated would give out the note above
mentioned, while on the other hand, if that note were sounded
in air at a distance, the incident vibrations would throw the
strings into vibration, and consequently would themselves be
gradually extinguished, since otherwise there would be a creation
of vis viva. The optical application of this illustration is too
obvious to need comment. — G. G. S.
XXVI. Observations on the Theory of Equations of the Fifth
Degree. By James Cockle, M.A., F.R.A.S., F.C.P.S. ^c*
[Concluded from vol. xviii. p. 510.]
75. A DAPTIXG the Eulerian or Bezoutian formulae to the
-^^ trinomial, and eUminating c and d, we find (compare
art. 44, note)
(t^b* + d%^-Qa%^-^a'^b + ^'-'a = 0, (e')
dfl«i6 + a6A4-3^Vi-'^-d4i2_.&3^4^0, (f)
+ 20dV63-^V=0. J- ' ' \S)
76. Form the equation
■ (_^i2+^6-fl^-Q-^--7)(e') + (f') = 0;
\ a a^ a^ a'/
the result, cleared of fractions, is
77. Form the equation
the result, cleared of fractions and divided by b^, is
(a»o + Q3a'^ + 2^5)03^3 +(2ai« + Qd«5 + d^) ^b^ 1
- (Qa^^ + Q'-&a' + Q-^^ - 2>b'a'>)a% - (a'o + 2Q^a'^ + ^ •)■&«*» = 0. J
* Communicated by the Autlior.
Phil. Mag. S. 4. Vol. 19. No. 126. March. 1860. P
198 Mr. J. Cockle on the Theory of Equations
78. The elimination of b between these results may be ex-
pressed by the determinant
«>
/3a%
rfa\
^a%
Ba\
ea,
7«^
ea,
Ka,
in which a, /3, . , , ^ are functions of a^ and of ^. This deter-
minant is of the form ;)^(^, a^)a^, and rejecting the factor a^, the
result of the elimination of b will be of the form
79. A result of the same form will be obtained if we eliminate
b between (g') and (e') or (f ') ; for 0 can only appear in the final
results of elimination under the form 0'^, otherwise we should be
led to equations one side of which would have five times as many
values as the other.
80. Further : the formulae of Euler and Bezout are not affected
by the binary interchange ^a d\ ^b cY and we obtain, at pleasure,
four systems of relations, which, for brevity, I shall write
{a, b, ^) = 0, {d, c, b) = 0, (c, a, - h) = 0, (6, rf, — ^) = 0 ;
and these systems show that a and d are inseparably connected
in the formul&e, and that the ultimate results will assume the
form of quadratic equations. And such is the form which the
equations in u and v (art. 44) indicate.
81. Let, then,
denote the result of eliminating b, c, and d from the equations of
art. 75. This result is equivalent to
and, solving as for a quadratic, we find
©5 = ^+ -//X^-S^O^,
or, as we may write it,
05 = ^+ A/y,
82. That X and (j, are rational functions of ^, follows from the
consideration that
2/^={©')^+(0'")^
and consequently that fju and ^ are " similar " functions. Hence
we may express /x in terms of ■& by the process appropriate to
such functions, or we may adopt Lagrange's method of division.
of the Fifth Degree. 199
But the preferable course will be to proceed by elimination as in
the present* discussion.
83. Let fjJ and 1/ be the values which /i and v take when P— ^
is substituted for ■&. The indicated form for the root of a general
quintic is
+ r 't/;:ir7? + i"" ^7^=~v9 } •
84. This expression coincides in substance with that differ-
ently deduced by Mr. Jerrard in his ' Essay/ It embraces the
second solvable form of Euler {Novi Cumm. Petr. p. 96 et seq.),
as it probably may be made to do that of Abel (posthumous
theorems, Crelle, vol. v. p. 336). It embraces also the first
soluble form of Euler as well as that of Demoivre, and the one
that I have calculated by making one only of Lagrange's func-
tions vanish (Diary for 1858).
85. The vanishing of this function is marked by -&=0, and
the roots of the form last mentioned are comprised in the ex-
pression f
i'"-v/(10B-A-5Q)P-E
v^^-f:v(f
+'-"'\/^ + ^+a/(^ + ^)'-i»
86. Presumably ^4 is a rational function of dj, and indeed I
* The mode of elimination that I have found to be the most convenient
iu practice is Newton's, in which we annihilate extreme terms alternately.
The process used in the text is a modification of Newton's, arrived at thus ;
Let X and Y he of the mth and 71th degrees in the quantity to be elimi-
nated, and let Xj and X2 be indeterminate expressions of the (k — wi)th
degree in the same quantity. Form the expressions
XiX+Y and XjX+Y,
and assign the indeterminate coefficients so that the first n — m-\-\ terms of
the former and the last n — /n+l of the latter shall vanish. If we make
the unmodified method of Newton gives the cubics
/V6'— 432(/a5 + 2a-')a''i='-2%6-|-92(/^_4&V)a»=0,
(/^_494a5)a^6H29/a"i2_433(^^_,.2aio)a3j_^232_0
in place of those in the text.
t A and B (which I call respectively v and u in the ' Diary ') are known
and rational, but complicated functions of the coefficients. Compare art. 21
of Mr. Harley's paper on Symmetric Products in the Manchester Memoirs,
vol. XV.
P2
200 Mr. J. Cockle on the Theory of Equations
have inferred that it is (arts. 58, 59). The presumption is now
rebutted. But since -5^ replaces ■& in the formulse, we have to
inquire whether ^^ be a rational function of ^{'. If it be, then,
since every root of a rational equation is a rational function of its
own square (for the equationmay be written a^^(a'^) 4-A/r(,r2) = 0),
we see that 6^ must be a rational function of 6^^, and ^4'^ of O^^.
Consequently each of the expressions
must be a symmetric (and indeed rational) function of the roots
of the given quintic. Hence it is readily seen that the cubic
whose roots are the above three values of 6^ On will have all its
coefficients symmetric in w, and therefore invariable under all
interchanges of the .^-'s. It would follow that 6^ Ol has only
three values ; and that for some one value (at least) of r and s
we have 61=6',
an inadmissible result.
87. The same difficulty presents itself in another shape.
Since all functions of the above form are invariable under inter-
changes of the x's, the doctrine of similar functions shows that
the second coefficient of the cubic could only be determined by
the solution of a quintic, even if the first were known. But
inasmuch as one of the most distinguished of writers on the
theoi-y of equations has recently repeated the expression of a
belief, formed many years ago, that the general quintic is soluble
by means of an Abelian sextic, I shall add a few words upon the
point.
88. Let Y:,, = a6,'e,^ + b6,'6^^+..+ed,6,+f,
then, as* we know,
V,,4 + V2,6 + V3,5=/-,(.r5),
where j\ denotes a rational function. Let the ratios of o, 6, . . , e
* Recurring to arts 14 et seq., and grouping the 6's thus,
1^, ^(a(/)|, {^(aby ^(C(/U, {Bfa cy 6rbd\^,
the omitted interchange (bc'\ being equivalent to (ad\ and the inter-
changes in each of the other groups being complementary, let every single
interchange be applied. The order of the grouj)s will or may be changed,
but the members of each group will be inseparable. Consequently no pos-
sible interchange can, save as to the order in which they are written, aifect
the groups. And since (see art. 15) the form of 4> is arbitrary, and we may
make
(f)=x^+axi + bx.^+cx3+dx^,
we see that many of our coiclusions are true, whatever be the values of a,
b, c, and d. It is when we seek a symmetric product that those quantities
become unreal fifth roots of unity, and that 0 becomes one of the func-
tions of Lagrange and Yandermoade.
of the Fifth Degree. 201
to / be so assigned that Xc, may disappear from r^, in other words
that rj(<r5) may be a symmetric function, say r,(0), of or. We
may form the cubic
V3_r,(0)VHr2(.r5) V-r3(^5) =0,
the roots of which will be the abov e three values of V.
89. If x^ does not disappear from i\ and 7-3, the determination
of those functions depends upon the solution of a quintic, and
cannot be attained. If it does disappear, the cubic becomes
V3_r,(0)V2 + 7-2(0)V-r3(0)=0.
90. In the latter case, since ;-(0) is not affected by any inter-
change of the a's, of the fifteen values of V,, ,. three only will be
distinct. But (art. 63) this involves the relation
V =:V
which is equivalent, for some finite value of 72, to
91. But no such relation exists among the roots of the sextic
in 6, and no such cubic can be formed the coefiicients of which
shall be symmetric functions oi x; and since the 3 of Mr. Jer-
rard and my 6 are similar functions [fonctions semblables), I am
constrained to conclude that the supposed cubic of that eminent
algebraist cannot be formed, and that the supposition that the
general quintic is soluble by an Abelian sextic involves the untenable
supposition that the sextic in 6 has equal roots, or roots some inte-
gral poivers of which are equal.
92. In perfect accordance with this conclusion is that dedu-
cibje from the symmetric product, 'rr[d), of the sextic in 0. We
find, by substitution in the formula which I have already* given,
that
iT{e) = ^(108Q5- E3)2(5'0E)2,
and that when ir vanishes and cubic radicals appear, the sextic
and the given quintic have each equal roots.
93. So, too, although I have succeeded in obtaining unsym-
metric functions of 6 which are symmetric in x, and therefore
known, the doctrine of similar functions shows that these known
quantities can only be applied to the solution of the sextic through
the medium of a quintic.
94. The /3 and a roots of the 15-ic in 7 can be obtained, or
at all events verified, by a process resembling that employed in
art. 72 for the other roots. But
is the type of the formulae of verification ; and ^ and « are the
* Phil. Mag. May 1858, p. 3SK)
202 Mr. J. Cockle on the Theory of Equations
roots of a 10-ic equation, each root of which is a rational and
symmetric function of two roots of the given quintic.
95. Again, we may (art. 56) express ^4 as a rational function
of ©1 ; and if for a moment we write
«J "J®/'J = "^^^ v°' y± ^-^ '^" "5 j'
*J ~j.©/"J = ^P-"^iV<^os 5-± V -1 sin -j,
then ^4 expressed in terms of -^i is
^4r=:P + ^,M + 2cos-— ] — 2(P— ^j) COS — - ± 4^i sm ^sin-p-;
and if we elevate each side of this equation to the fifth power,
expand and eliminate m and m' by means of
cosm=-^, cosm'= — ~ — r,
9,4 (P-9,)«'
we shall have one of the actual expressions on which the fore-
going and (virtually) Mr. Jerrard's argument is founded. As to
my own particular view (arts. 58, 59), I may add that if ^4 were
a rational function of ^j, the roots of the quintic would contain
no quintic surds unless (which there is no reason to suppose,
though I once suspected it) the theory of Abelian sextics is im-
perfect. The error of Mr. Jerrard inheres, in my opinion, in his
mode of comparing the equations (ab) and (ac) at pages 80 and
81 of his most valuable ' Essay .^ His functions jH, sS, 3S, and
4H in art. 104 are foreign to the question, mere instruments for
eliminating radicalities. They lead to no other result than that
to which the immediate comparison of (ac) and
S-oS = 0
would conduct us, viz. an expression for S into which P/y/Se)
enters irrationally.
96. The theory sketched in these papers has been developed
in pages* more appropriate than the present to the details of
mathematical processes. I would suggest that x may be ex-
pressed as a rational function of y, and yb as an irrational func-
* See a paper " On the Theory of Quintics," by the Rev. Robert Har-
ley, F.R.A.S. &c., in the Quarterly Journal of Pure and Applied Mathe-
matics, January ISfiO. M. Wantzel's argument will be found in M. Serret's
Cours d'Algebre Superieure (2rae ed., Paris, 1854).
of the Fifth Degree. 203
tion of 9 ; for
(52^)2_52P(52^) = ^.
The object of research will not be a finite algebraic solution ; but
I have ascertained (and it may be worth noticing) that the par-
ticular form
a;5_5Q^2_^2Qv^Q2=0
is soluble by radicals.
97. The present discussion, then, seems to me to establish
the insufficiency of two proposed methods of solving equations of
the fifth degree, or rather equations in general, and to add to
the moral evidence of the impossibility of the solution. Perhaps
the want of universal assent to the argument of Abel may in
some degree be owing to the want of uniformity in the views
taken by Abel himself, by Sir W. R. Hamilton, by M. Kronecker,
and by Galois, and it is unquestionably desirable that that argu-
ment should be simplified. But I do not think that M. Wantzel^s
modification of it meets the desire. The formulae in his second
step should^ I think, be replaced by
<p[x^ Xq, a?|, a?4 . . . j = « 0('^i> "^2^ "^a* ^4 • • • )^
<P\X^ x^y x^, x^ . . . ) = ct (pyx^} x^ x^y Xj^. . .),
</)(^i, x^x^x^...) = a'^</)(a;3, x^, x^x^...),
the only inference from which is
ot\+\+y.— \^ or l+A, + /^ = 0(mod. n).
That n=3, \=1, /x=l cannot, I think, be inferred without
previously showing that the only prime power of an unsymme-
tric function which can have two values only is a cube, and we
are once more remitted to the arguments of Abel and Sir AV. R.
Hamilton. W. Wantzel's third step, too*, seems open to objec-
tion. Perhaps the impossibility of cubic radicals entering into
the root may afford the basis of the desired simphfication.
4 Pump Court, Temple,
February 6, 1860.
* The cyclical interchanges of five do not coincide with the cycUcal in-
terchanges of three ; and we can only infer that
where the symbols on the right refer to the quinary, and those on the left
to the temarj' interchanges.
[ 204 ]
XXVII. On the Equilibrium and Motion of Liquids in Porous
Bodies. By ]\I. J. Jamin*.
THE function performed by vegetables, which consists in the
raising of water tlu'ough their tissues to their leaves, has
never yet been explained. This effect, however, must either be
due to the play of special organs analogous to the human heart,
or it must be determined by the exercise of molecular forces and
gravity in the ligneous body. If the first hypothesis were true,
physiology would, in all probability, have detected at least the
existence of the supposed organs; from its silence, therefore,
w^e are led to conclude their non-existence. On the other hand,
if the second hypothesis holds good, the question enters the
domain of general physics, and may with justice be studied ex-
perimentally with a view of imitating artificially this function of
vegetables.
Regarding the problem from the latter point of view, M.
Jamin announces having arrived at a plausible solution. In this,
his first communication, however, the author occupies himself
solely with certain preliminary phaenomena of capillarity in tubes
and porous bodies; he proposes subsequently to apply the
principles he here establishes and to describe an apparatus, ex-
clusively composed of inorganic substances, which in its struc-
ture presents a striking analogy to that of vegetables, and which
possesses the property of raising water, as trees do, to a height
greater than that of the atmosphere between a moist soil, from
which this water is continually drawn, and the artificial leaves
where the water is continually evaporated. The conclusion he
announces is that capillary forces suffice to explain the motion
of the sap in vegetables.
A capillary tube being taken, one of its extremities is put
in communication with a vacuum ; by so doing a current of air is
established within the tube from the atmosphere to the vacuum.
If then the finger, covered with wet linen, be alternately pi-essed
against, and lifted from the free extremity of the tube, the opera-
tion being frequently repeated at very short intervals, columns
of liquid separated by bubbles of air will traverse the tube with
a velocity which, from being very great at first, will diminish as
the operation proceeds, and finally become zero. A chaplet whose
beads are air and water is thus obtained, and the apparatus thus
prepared is found to possess peculiar properties.
When a pressure is exerted at one extremity the nearest beads
recede quickly, the following ones are less displaced, and the
more distant ones I'cmain unmoved. By doubling the pressure
twice as many beads are put in motion ; or, more generally, the
* From the Comptes Rendus, January 23, 1860.
On the Equilibrium and Motion of Liquids in Porous Bodies. 205
number of beads to which motion is imparted is proportional to
the magnitude of the pressure apphed. Consequently the oppo-
site extremity of the column only begins to be displaced when
the difference between the pressures acting at its two extremities
reaches a limit proportional to the number of beads in the
column ; and if this number be increased indefinitely, the limit
in question will also be indefinitely increased. In this manner
a pressure of three atmospheres, acting incessantly for fifteen
days at the extremity of a very fine tube containing a great
number of beads, failed to produce the least visible displacement
of the liquid.
Inversely, when a partial vacuum is produced at one end of
the tube the nearest bubbles of air dilate greatly, the interme-
diate ones less, and those furthest distant remain unaffected so
long as the dim.inution of pressure does not exceed a limit pro-
portional to the number of bubbles or beads. To make the ex-
periment, a very long tube containing a great number of beads
may be cemented into the upper part of a barometer-tube. The
mercury will then maintain precisely the same position as it
would do if the tube were perfectly closed.
This experiment shows that the pressure exerted at one ex-
tremity diminishes abruptly by a constant quantity at each place
where the continuity of the column of liquid is interrupted ; and
this fact may be easily explained.
For it is probable that the first effect of the pressure H' is to
alter the form of the nearest bead of liquid, by hollowing out its
anterior surface and increasing the radius of curvature of the
meniscus which bounds its posterior surface. A portion, L, of the
pressure being thus expended in the deformation of the first
bead, a deformation which cannot exceed a certain limit, and
which is the same for all the beads, the residual pressure H' — L
is transmitted by it to the next succeeding air-bubble, and thus
to the second bead, which, in becoming similarly deformed, again
diminishes the pressure by the same amount as before. This
action continues until the originally applied pressure has, by n
equal, successive decrements, one at each bead, become reduced
to 11' — nL=lI, the normal pressure in the tube, when, of
course, equilibrium results.
By generalizing this idea, it is easy to show that the chaplet
may assume an infinite number of states of equilibrium, whose
conditions may be calculated ; and experiment is found to verify
the results of calculation.
It will be at once seen that these properties must considerably
modify the ascent of liquids in capillary tubes. There arc in
fact two cases to be distinguished.
First. After raising the tube in the liquid in which one end is
206 On the Equilibrium and Motion of Liquids in Porous Bodies.
immersed, and allowing the column of raised liquid to descend
to its position of equilibrium, the length of the raised column is
a + nh, and consequently greater the greater the number n of
interruptions ; this length may increase indefinitely.
In the case where the weight of each bead is equal to L, they
are individually in equilibrium, and a column of indefinite
height, interrupted only by very small bubbles, and everywhere
at the atmospheric pressure, may be sustained.
Secondly. When the tube is depressed in the bath, and the
liquid allowed to rise to its position of equilibrium, the length of
the raised column is diminished in proportion to the number of
bubbles, and becomes a—nh; it is always less than if the column
were continuous, and it may become negative and decrease inde-
finitely.
In accordance with theory, experiment also proves that when
once a column of liquid, whose length is between the limits a + nJj
and a — nh, has been placed in the tube it will remain there.
Some experiments were also made with a view of measuring the
limit L of the resistance which a single bead can oppose to the
pressure. It was found that this limit is independent of the
length of the bead, but that it increases when the bubbles of air
diminish ; it increases, too, very rapidly when the diameter of
the tube is diminished, and is equivalent to 54 millims. in a tube
where the capillary ascension amounts to 200 millims. In such
a tube, therefore, four interruptions are equivalent to the capillary
force, and may annul the latter when the liquid rises, or double
the height of the sustained column when the liquid descends.
Mercury produces efi'ects much more intense, but alcohol and
oil oppose no resistance to pressure.
When a capillary tube, instead of being cylindrical, possesses
successive contractions and expansions, it exhibits still more
curious properties. After being once moistened, the thin film
of liquid which remains adhering to its walls soon collects at the
contractions, and thei'e forms interrupted beads. Here then a
chaplet is formed, as it were, spontaneously, and in consequence
of the nature of the canal, the above-mentioned properties of a
cylindrical tube become exaggerated in a surprising manner. A
tube with eight very narrow contractions sufficed to close a baro-
meter-tube hermeticaUy, and even to overcome a pressure of two
atmospheres.
If pressure be applied to one extremity of such a tube, filled
with water, the latter overflows {filtre) without difficulty ; but if
this pressure is exerted on a compressed gas, the latter replaces
the water in each successive chamber, and leaves a bead of liquid
at each contraction ; these beads, by opposing a resistance which
increases with their number, finally destroy the pressure.
MM. Deville and Troost on Vapour densities. 207
Inversely, when the tube is full of air and a column of water
is forced into it by pressure, it fills the several chambers suc-
cessively, destroys the beads, and annuls their resistance ; finally,
it fills the whole tube and commences to overflow.
These consequences may be applied to porous bodies in which
we may assume the existence of canals alternately narrow and
broad. When a porous vessel, such as is used in the battery,
or an alcarraza, or a plaster statuette, or any other cavity formed
in a porous mass is filled with water, any pressure exerted upon
this water causes the same to filter through the mass ; on the
other hand, however, a perfect vacuum may be formed in the
interior, atmospheric air being incapable of penetrating through
the walls when moistened.
When both surfaces are immersed in water, and a pressure is
exerted in the interior by means of compressed air, the latter, in
the first place, expels all the water ; but when this is accomplished,
the air does not filter through the walls : the pressure, indeed,
may be increased to two, three, and in some cases even to four
atmospheres without causing the least air-bubble to traverse the
porous sides ; and this pressure, too, may be maintained for an
indefinite period, exactly as if the sides of the vessel were not
traversed by capillary fissures.
XXVIII. Chemical Notices fi'om Foreign Journals. 5yE. Atkin-
son, Ph.D., F.C.S., Teacher of Physical Science in Cheltenham
College.
[Continued from p. 126. J
IN continuation of previous researches, Deville and Troost*
have made some determinations of the specific gravities of cer-
tain vapours at high temperatures. The vessels used were por-
celain flasks with narrow necks, of 280 cubic centims. capacity.
These flasks are loosely closed by means of a small porcelain cy-
linder of 1 or 2 millims. diameter, which fits in the neck. At the
termination of the experiment, the projecting end of this cylinder
is fused by the oxyhydrogen lamp and closed cft'ectually. The
bath employed was that previously described, in which high con-
stant temperatures are obtained by means of metallic vapours. In
these experiments, Deville and Troost used cadmium vapour, the
temperature of which is 860° C, and zinc vapour, the temperature
of which is 1040° C.
The determinations were made by taking the density of the
substance operated upon, and that of iodine under the same
circumstances. Deville and Troost obtained in this manner a
* Comptes Rendus, vol. xlix. p. 239.
208 M. Bineau on Vapour-densities.
very accurate relation between the densities of the two vapours,
the density of one of which is perfectly well established.
The results arrived at were as follows : —
Sulphur. — The vapour-density of this substance at 860° is 2*2.
For the temperature 1040° the same number was also obtained
in twelve successive experiments. Previous determinations of
other experimenters had furnished the number 6-6, which gave for
sulphur an atomic value ^ that of oxygen^ phosphorus, &c.
Various explanations have been oflFered to explain this anomaly,
which is removed by Deville and Troost's obsei-vations.
Selenium. — Its vapour-density at 860° is 8-2 ; at 1040° it is
6'37. Theory and analogy with sulphui* require the number
5-44. By making the determination at 12° to 1400° C, the
authors hope to obtain this number.
Phosphorus. — Vapour-density at 1040°, 4*8. Calculated, 4*4.
Cadmium. — At 1040° the vapour-density is 3*94. For a
condensation to two volumes the number 3*87 is required.
Chloride of Ammonium. — At 1040° the observed vapour-density
was 1"01. For a condensation to eight volumes the number
3*87 is required.
Bromide of Aluminium. — Vapour-density 18'62. Theory
requires 18*51.
Iodide of Aluminitim. — The observed vapour-density was 27"0.
The number required by theory is 27*8.
Bineau has also published* some determinations of the densities
of superheated vapours, executed upwards of ten years ago.
The experiments were made in tubes placed in a sort of cylin-
drical iron case, from which the finely drawn out extremities of
the tubes projected. The capacity of each tube was determined
before the experiment. The tubes were sealed by means of an
oxyhydrogen flame. The tubes were covered with an argillaceous
lute, and were surrounded by sand, or iron filings. The cylinder
was placed horizontally on a grate, and heated as regularly as
possible ', the temperature was determined by means of an air-
thermometer ; and in order to test the method, a control deter-
mination of the density of mercury was made. It gave the
number 6*7, which agrees well with 6*97, the number obtained
by Dumas, and 6*91, the calculated number. A control deter-
mination of the density of iodine gave the number 8"65. Dumas
obtained 8'716, and the calculated number is 8*8.
The numbers obtained for the density of sulphur vapour varied
in nine experiments between 2*1 and 2*8. These experiments
may be divided into two groups ; in one of these the temperature
was below 800°, and the numbers were —
* Comptes Rendus, vol. xlix. p. 799.
M. Berthelot on New Alcohok. 209
results were
Vapour-density.
Approximate temperature.
2-8
714°
2-7
727
2-6
731
2-8
743
experiments, where the temperature excee(
re —
Vapour- density.
Approximate temperature.
2-4
834°
2-6
851
2-4
963
2-1
1082
2-3
1162
At 450^ to 500°, Dumas obtained the number 6*56, and
Mitscherlich 6*9. Biueau assigns to sulphur vapour at 600° the
density 5; at 700°, 2'8; and at 800°- 1000° the density 2-2,
which is the number obtained by Deville and Troost.
Berthelot has published* a detailed account of a series of
experiments, preliminary notices of which have already appeared,
in which he shows that cholesterine, meconine, and Borneo
camphor belong to the class of alcohols. He considers an al-
cohol to be a neutral substance, consisting of carbon, hydrogen,
and oxygen, which unites directly with acids, under elimination
of water, to form a neutral compound, which by assimilation of
the elements of water is again resolved into the substances of
which it was composed.
The neutral ethers of the above substances are obtained by
heating them with acids, in sealed tubes, for several hours, to a
temperature of 200°, and then purifying the resultant substance
by appropriate methods.
Cholesterine is considered by Berthelot to have the formula
Q52 JJ44 Q2^ jjj-^jj ^Q belong to the series of alcohols whose general
formula is C" H^-'O^, and to which cinnamic alcohol, C'^ H'o O^,
belongs. Cholesterine forms compounds with stearic, butyric,
and acetic acids, as also with hydrochloric and benzoic acids.
The stearic acid compound, C^^ H'^ 0, C^ H^^ 0^, is a white body
crystallizing in small brilliant needles. It melts at 65° to a
colovirless liquid which solidifies to a dull, uncrystallinc waxy
mass.
With spermaceti, which has long been recognized as an alcohol,
Berthelot has prepared the stearic, butyric, acetic, and benzoic
compounds. With the exception of the benzoate, they are
difficult to obtain pure.
* Annates de Chimie et de Physique, vol. Ivi. p. 51.
210 M. Berthelot on New Alcohols,
Meconine, C^^H'^O^, also forms an ether when heated with
stearic acid. It is a neutral, solid, colourless substance, and is
readily fusible. It has the formula C-*^^ H'^^ 0^^; and its forma-
tion may be thus expressed :
C^o H 10 OH 3 C36 H36 04 -4 HO = C^^ H^^ O^^.
Meconine. Stearic acid. New body.
Meconine appears to be a biatomic alcohol; and Berthelot
considers that it stands in the same relation to its oxidation pro-
ductSj opianic acid and hemipinic acid, as ethylene does to alde-
hyde and acetic acid.
Meconine. Ethylene.
CsoHioQio C^H^O^
Opianic acid. Aldehyde.
C20 JJIO 012 C4 H^ 0"
Hemipinic acid. Acetic acid.
Borneo camphor, C^*^ H^^ 0^, according to Berthelot, stands in
the same relation to ordinary camphor, C^*^ H^^ O^, as benzylic
alcohol, C14 W 0\ does to hydride of benzoyle, C^^ H^ 0^. Ordi-
nary camphor is an aldehyde ; it does not combine with acids ;
when it is heated with potash in a sealed tube for a long time
at the temperature 180°, it is resolved, thougli with difficulty,
into borneole (Borneo camphor) and a new acid, camphic acid,
which probably has the formula C^° H^^ 01 The decomposition
would be thus expressed :
2C20Hi6OH2HO = C20Hi8OHC20Hi6Ol
Camphor. Borneo camphor. Camphic acid.
The artificial Borneo camphor, or camphole, has all the pro-
perties of the natiu'al substance, excepting that it deviates the
plane of polarization more strongly. Camphole combines with
hydrochloric acid at 100° and with organic acids at about 200°.
The stearate is a neutral, viscous, colourless, inodorous oil which
sometimes crystallizes. The hydrochlorate, C'^*^ H^^ CI, has all the
physical properties of the substance isomeric with it, pi'oduced
by the combination of hydrochloric acid with oil of turpentine,
and known as '^ artificial camphor.^'' Unlike this compound,
however, the hydrochlorate of camphole is readily attacked by
alcoholic alkalies. Camphic acid is very difficult to purify. Its
formula is probably C^^Hi^C*; it is obtained as an almost
solid colourless mass, heavier than water, in which it is insoluble.
In the free state it is decomposed by heat. It is acted upon by
nitric acid with formation of a nitro-compound. Camphate of
soda produces precipitates in most of the metallic solutions.
MM. Strecker and Moller on VulpicAcid. 211
Berthelot also examined the action of organic acids at a high
temperature on orcine, thymole, alizarine, and the hydrates of
oil of tm'pentine. All these substances, with the exception of
orcine, contain 20 equivs. of carbon. Orcine, C^"* H^ 0"*, appears
to form a compound with stearic acid. The experiments with
the other substances led to no positive results.
Vulpic acid, one of the lichen acids first isolated, and found in
the Cetraria vulpina, was so little known that its identity as a
distinct acid was doubted. Moller and Strecker* have recently
investigated it, and have arrived at some very interesting results.
The acid is prepared by macerating the lichen with lukewarm
water containing milk of lime, and supersaturating the extract
with hydrochloric acid ; a precipitate is formed which is washed
with cold water and dissolved in boihng alcohol. On cooling, the
acid crystallizes in tolerably long needles of the monoclinic system,
which in colour and lustre resemble sulphin*. Its best solvent
is chloroform, by which it may be directly extracted from the
lichen. Its formula is C^^H''*0^°, and it is monobasic. It
forms crystallized salts with potash, ammonia, lime, and baryta.
The salts of the heavier metals are obtained by the double de-
composition of vulpate of potash with the corresponding metallic
solutions. In appearance vulpic acid most resembles usnic acid ;
and their composition only differs by the elements of water, the
formula of usnic acid being C^^H'^0^'*; but in their chemical
deportments there is considerable divergence.
When vulpic acid is boiled in a distillation apparatus with
baryta water, oxalate of baryta is gradually deposited, and a
liquid distils over with the water, which is methylic alcohol. In
the residual liquor from which the oxalate has precipitated, the
soluble baryta-salt of a new acid is contained. It is obtained
thus : the excess of baryta is removed by carbonic acid, the liquor
filtered, concentrated, and supersaturated with hydrochloric acid.
A crystalline substance separates, which, when recrystallized from
alcohol, forms beautiful thin rhombic plates, which molt at 76°*5
and distil at 265°. This substance is strongly acid; it forms
salts with alkalies and alkaline earths, which, however, from their
great solubility, are difficult to crystallize.
The composition of the acid is C^^H^O*, which is that of
the toluylic acid obtained by Noad by oxidizing cymole by nitric
acid. But the two substances are only isomeric, and not iden-
tical; forNoad's acid crystallizes in needles, and melts above 100°.
This new acid, which has been named alphatoluyUc acid, agrees
closely in its properties with the toluylic acid obtained by Can-
nizaro by boiling cyanide of benzylc with potash.
* Liebig's Annalen, January 1860.
212 M. Kolbe on the Synthesis of Salicylic Acid.
Alphatoluylic acid is oxidized, but with difficulty, with forma-
tion of hydride of benzoyle. Strecker and Moller have prepared
the chloride, the amide, and the nitro-compound of this acid.
They represent its formation from vulpic acid in the following
manner : —
Vulpic acid. C38 H^^ Oif>l 2 eq. Alphatoluylic acid C^^ R^^O^
+ 8eq. water H^ 0^ L= Oxalic acid . . C"* H^ 0^
C38H22 018J Methylic alcohol. C^ H^ 0^
C38H22 018
If, in the decomposition of vulpic acid, potash be used instead
of baryta, other products occur. Methylic alcohol distils over ;
and when the residue is supersaturated with hydrochloric acid,
carbonic acid is disengaged in abundance and a crystalline pre-
cipitate formed. This is a new acid, which, when recrystallized
from boiling alcohol, appears in the form of rhombic prisms. The
crystals are brittle, but tolerably hard ; they melt at 154^; they
are difficultly soluble in water, but readily so in alcohol. The
formula of this acid is C^'^ H'^0^; and the authors name it oxa-
toluyJic acid. The baryta-, silver-, and lead-salts are all crystal-
lized, and are monobasic. Oxatoluylic ether, C^"^ H'^ (C** H'^) 0^,
is best obtained by the action of iodide of ethyle on the silver-
salt. It forms colourless prismatic crystals, which melt at
45°'5. By the action of nitric acid on the acid, a nitro-compound
is formed. The formation of oxatoluylic acid is as follows : —
Vulpic acid . C^^Hi^Oio^ C^^H'^O^ Oxatoluylic acid.
Water . H^ 0^' 1 = 0- H^ 0^ Methylic alcohoh
(^38 JJ20 0^^ J C'* 0^ Carbonic acid.
C38 H20 QIS
^\Tien boiled with strong potash, oxatoluylic acid readily un-
dergoes a further change ; it becomes converted into oxalic acid
and toluole. From this deportment it appears to have received
its name. The decomposition may be thus expressed : —
C32Hi«0« + 2H0 = C'*H2 08-|-2Ci4H8.
Oxatoluylic acid. Oxalic acid. Toluole.
The difference in the decomposition of vulpic acid by potash and
by baryta is remarkable as showing a great mobility of the atoms.
It appears probable that the insolubility of oxalate of baryta is
the determining moment in the first reaction, as is frequently
observed in double decompositions of salts.
Salicylic acid, C^'* H^ 0^, has been considered by Kolbe to have
a constitution analogous to that of carbovinic acid ; in short, to
be carbophenylic acid, —
M. Scherer on Xanthine and Leucine. 213
Carbovinic acid . . ^^S^qI^'^''
Carbojjlienylic acid . H O i ^^ ^^'
This view is supported by the well-known fact that salicylic acid
decomposes, when heated with powdered glass, into phenylic
alcohol and carbonic acid.
Kolbe and Lauteinann* have recently effected the synthesis
of this acid from phenylic alcohol and carbonic acid. It is not
formed when carbonic acid is passed into sodium-phenylic
alcohol, C'^H^NaO'-; but when carbonic acid is passed into
phenylic alcohol while sodium is being dissolved in it, the three
bodies unite \vith liberation of hydrogen to form salicylate of
soda. On neutralizing this product with hydrochloric acid, and
boiling with water to expel excess of phenylic alcohol, salicylic
acid pure and in tolerable quantity is obtained.
By analogous methods these chemists hope to obtain from
hydrate of cresyle and hydrate of thymole the corresponding
acids, and from bisulphide of carbon and hydrated oxide of phe-
nyle the compound
TT Q VC^S'* (Phenylxanthogenic acid).
In some recent experiments with flesh, Scherer t has found
that xanthine % is contained in muscle, and also in the pancreas.
In the former it exists along with hypoxanthine, whicli he has
shown to be identical with Strecker's sarcine ; in the pancreas
it exists along with guanine. The pancreas contains about
0"0166 per cent, of xanthine, and 0-01223 of guanine. It is
accordingly a better source for xanthine than flesh, which only
contains 0*003 per cent.
Scherer has also observed that leucine is contained in the pan-
creas, and in such large quantities that the latter is the most valu-
able source for it. The following experiments will show how it is
obtained therefrom. Twenty pounds of finely chopped pancreas
were boiled in water for about five minutes, the mixture filtered,
and the residue treated with hot water. The filtrate was pre-
cipitated by baryta water, filtered, and the filtrate evaporated on
the water-bath with the addition of acetate of copper. The pre-
cipitate formed, which consisted of xanthine and guanine in com-
bination with copper, was filtered off. On saturating this fil-
trate with sulphuretted hydrogen, and evaporation, the liquor
yielded about six ounces of pure leucine containing mere traces
* Liebig's Annalen, January 1860. f Ibid. December 185.9.
+ Phil. Mag. vol. xviii. p. 135.
Phil Mag. S. 4. Vol. 19. No. 126. March 1860. Q
214 MM. Schmidt and Stiirzwage on the Effects produced
of tyrosine. This quantity corresponds to 177 per cent, of the
fresh pancreas, or, since that contains 76 to 77 per cent, of water,
to 7"37 per cent of the soUd constituents. A subsequent experi-
ment, made with a fresh pancreas under special precautions,
showed that leucine pre-existed in the gland, and was not a pro-
duct of decomposition.
Professor Schmidt and Dr. Stiirzwage in Dorpat have made
a series of experiments on the action of arsenious acid, when in-
troduced into the circulation, on the oxidizing process in the
body. The mode of experimenting consisted in determining the
normal quantity of carbonic acid exhaled in an hour by certain
animals (fowls, pigeons, and cats), and then administering to them
arsenious acid, and again observing the quantity of gas exhaled
in the same time. The apparatus consisted of a bell-jar, stand-
ing on a ground-glass plate, under which the animal was placed.
In the tubulure of the bell-jar were inserted two tubes, and a
delicate thermometer. One of these tubes communicated freely
with the air, the other was connected with a series of tubes for
the absorption of carbonic acid and water, and with an aspirator
by which a regulated quantity of air could be drawn through the
system. Each experiment lasted about an hour, during which
time about 30 to 35 litres of air were drawn through : the car-
bonic acid of this air was determined by a separate experiment,
and allowed for. The secretion of urea was determined in some
cases : the determinations were made by Liebig^s method.
A fowl weighing 896 grms. was found to respire on an
average 2*07 grms. CO^ in the hour. A solution of 0*018 grm.
arsenious acid was then introduced into its crop, and after half an
hour the bird was placed under the jar. It was found to respire
1*88 grm. of CO^ in the hour. On the next day 0'027 grm. of
AsO^ were administered; the quantity of CO^ diminished to
1*35 grm. ; at the same time the bird was attacked by severe
diarrhoea, its respiration became greatly accelerated, it drank
much water, and trembled violently. On the following day
these symptoms diminished, and 0-035 grm. AsO^ were injected.
Three hours after, the expiration of carbonic acid diminished to
1*296 grm.
In an experiment with another fowl, the injection of 0*032
grm. AsO^ caused the respiration to diminish from 2'085 grms.
in the hour to 1*75 grm.
In another fowl weighing 1400 grms., the respiration of CO^
was 2*37. An hour and a half after the injection of 0*035 AsO^
it fell to 1"92 grm., and ten hours after to r37 grm. It showed
at the same time the usual symptoms of arsenical poisoning, but
afterwards gradually recovered, and in five days its respii'ation
by the administration of Arsenious Acid. 215
had reached the normal quantity. On administering the pre-
vious dose, the quantity diminished to 1'27 grm.
With a cat weighing 2"61 kilogs., and which consumed daily
130 grms. of flesh, the normal respiration was 3"08 grms.
0"025 grm. AsO^ were injected into the jugular vein ; the quan-
tity fell to 2*301 grms., and subsequently the animal died.
With another cat the average respiration of carbonic acid in an
hour was 2*925 grms., and the average amount of urea secreted
per diem was 9*85 grms. After the administration of 9*01 grms.
AsO^, the respiration sank to 1*98 grm., and the secretion of
urea to 361 grms.
With starving animals, previous investigations (by Bidder and
Schmidt) showed that the respiration diminishes in the first
forty-eight hours, but afterwards remains constant even until the
sixteenth day, notwithstanding the continuous decrease in weight
of the animal. To ascertain the efi'ect of arsenious acid upon
starving animals, the following experiments were made. A cat
whose respiration amounted to 3*3 grms., was left without food
for three days. On the first day the respiration had sunk to
2*45, and on the third to 2'24' grms. 0"018 grm. AsO^ were
then injected into the jugular vein. The respiration of CO^ de-
creased to 1*902 grm. The action of the heart also diminished
greatly.
In another experiment with a eat weighing 3*31 kilogs., and
fed on 150 grms. flesh daily, the respiration and the secretion
of urea were determined for four days. The animal was then
deprived of food, and the same determinations made for the
same time. The weight and the secretion of urea remained
constant for the first four days ; during the next four days the
weight diminished to 2*88 kilogs., and the respiration of carbonic
acid from 3*45 grms. to 2*54 grms. An injection of 0*005 grm.
AsO^ into the jugular vein was then made, and the animal fed
^vith meat, which it consumed with great avidity, but afterwards
vomited all but 24 grms. On the following day it refused food.
The respiration of CO^ diminished to 2*24 grms., while the bodily
weight slightly increased, and underwent no diminution until the
third day after the injection, during which time the animal rejected
all nourishment. This result is the more surprising since, in the
earlier period of inanition, fasting for twenty-four hours produced
a considerable diminution in the bodily weight.
From these experiments, Schmidt and Stiirzwage conclude
that arsenious acid introduced into the organism occasions a
considerable diminution in the secretion of matter. The pha;-
uomena are most observable in fowls ; but even in cats, wliich
vomit after the injection, and are to be considered as starving,
the diminution amounts to 20 per cent., even after eliminating
Q2
216 Prof. Dufour: Instructions fur the better observation of
the diminution caused by mere inanition. This fact explains
the fattening of horses after the administration of small doses of
arsenious acid, a fact well known to horse-dealers. That quan-
tity of fat, and of albumen, which corresponds to the depression
in the secretion of carbonic acid and urea, remains in the body ;
and if the animal receive adequate nourishment, its weight
increases.
XXIX. Instructions for the better observation of the Scintilla-
tion of the Stars. By Charles Dufour, Professor of Mathe^
matics at Morges*.
UNTIL lately the study of the scintillation of the stars has
not formed the subject of any series of observations.
Here and there may be found a few isolated directions, and
several persons have attem])ted divers explanations of the phe-
nomenon, but no continued observations have as yet been pre-
sented to the learned world. I believe I am the first who has
undertaken a work of this kind. My observations, commenced
at Morges in 1852, were at first but a series of gropings in the
dark, but since 1853 down to the present time, I have never
allowed one evening to pass in which the stars were visible,
without carefully observing the scintillation ; and after six years'
perseverance in the work, I am convinced that this branch of
astronomical study is important, and merits a place amongst
meteorological observations.
But in order that the results obtained may be more general
and more complete, it would be very desirable to undertake a
series of observations analogous to those I have commenced, in
other climates and under other meteorological circumstances.
At the time I am writing (December 1859) the following are
the stations where, I hope, a work of this kind is begun or con-
tinued.
Morges (Switzerland), 46° 30" North latitude and 4° 9" longi-
tude east of Paris. — Since 1853 I have taken at Morges nearly
24,000 observations on the scintillation of the stars. The prin-
cipal results obtained up to the present time, have been published
in the reports issued by the Academies of Belgium and Paris,
the ' Notices' of the Astronomical Society of London, and the
Bulletin de la Societe Vaudoise des Sciences Naturelles.
The Great St. Bernard, at an altitude of 2480 metres. — The
monks who inhabit this elevated spot all the year round, on the
borders of the eternal snow, have willingly undertaken to carry
on the observations that I commenced there in the summer of
* Communicated by the Author,
the Scintillation of the Stars. 217
1856, during the time I was staying at the hospital for scientific
purposes.
Grand Cairo, where Mahmoud Efi'endi, Director of the Ob-
servatory there, has ah*eady commenced, or will immediately com-
mence, a series of observations analogous to my own at Morgcs.
The Peak of Teneriffe, where Mr. Piazzi Smyth, Director of
the Observatory of Edinburgh, has already passed several months
for scientific purposes. This gentleman has promised me, that
if, as he hopes, he is able to continue his researches on this
isolated mountain, he will give special attention to the study of
the scintillation of the stars.
Severallocalities inRussia. — Last year the Geographical Society
of St. Petersburgh decided on publishing instructions for the
observation of all kinds of meteorological phsenomena, and j\I.
Kaemtz, who was charged with the direction of the publication,
requested me to draw up the part relating to the scintillation ; so
that I have reason to believe that in various parts of Russia,
observations in accordance with these instructions have already
been commenced.
Havanna, where M. Poey has founded an observatory during
the past year. This gentleman, with a view to observing the
scintillation at Havanna after my method, requested me to for-
ward him a copy of the instructions already sent to Russia ; so
that there also, I hope, the work is begun. But these stations
are very wide apart on the surface of the globe.
There are certain countries and certain climates from which
it is most desirable that observations should be taken ; for in-
stance, the Torrid Zone, as the observations taken at Havanna are
the only ones within the tropics. It would be well to have several
stations in various parts, as it is important to know what is the
amount of scintillation in the hottest and dampest countries in
the world. In the Austral Hemisphere also, observations would
be extremely valuable, because there not only would the student
have the opportunity of observing stars invisible to us (Acherner
and Campus among others), but the meteorological phrenomcna,
being notably different, would doubtless sensibly affect the scin-
tillation. Those beautiful stars of our own hemisphere also,
Sirius and Rigel, which we see only in winter, arc visible south
of the equator during the hot season, and are also nearer the
zenith ; and it would be interesting to know if their scintillation
is at all affected by these circumstances.
In countries situated to the extreme north, it would also be
extremely interesting and important to procure observations, and
to ascertain the amount of scintillation in those serene nights of
intense frost so constant in Eastern Siberia and even in European
Russia.
218 Prof. Dufour : Instructions fur the better observation of
If it were possible to procure observations from the Polar
regions during their long night of several months^ it would be
specially interesting ; and I would take the present opportunity
of recommending this branch of study to the notice of travellers
who may be passing one or more winters in the midst of the ice
of a Polar region. I regret exceedingly not having begun my
observations ten years sooner, as then those hardy mariners, who,
in search of Sir John Franklin, spent so many winters and tra-
velled over so great a portion of those regions, might perhaps
have been induced to devote some of their time to this branch of
study. But similar expeditions may be undertaken again ; and
if such should be the case, I promise myself to call the attention
of future explorers to this phsenomenon, in the hope of procuring
valuable results from their observations.
But in order to facilitate their efforts, and to avoid useless ex-
penditure of time, as well as to render the indications given by
one observer capable of being compared \vith the observations
made by another, I would recommend the use of the following
instructions, as the fruits of the experience acquh-ed in the long
series of observations taken by me at Morges.
1st. The manner of observing.
I have tried several scintillometers — all those indicated by
Arago, and a new one proposed by myself; but I am convinced
that none of them are worth the obsenations taken by the naked
eye. After a little practice it becomes easy to ascertain with
tolerable exactitude whether a star scintillates more or less than
another star, and to indicate the amount of scintillation by a
given number, in like manner as in meteorology the state of the
sky, or the force of the wind, is indicated by figures. Mj' own
method is to designate by 0 the absence of all scintillation, and
by 10 the highest degree, which is seen very rarely, and only
when the star is near the horizon, when it sometimes scintillates
very strongly, changes colour, and sometimes even disappears
and appears again. With a little practice it soon becomes easy
to distinguish degrees of scintillation even between 0 and 1,
1 and 2, &c. The next step is to ascertain the scintillation with
still more exactitude, and to designate it as O"^, 1*6, &c., though
it is scarcely possible to subdivide these degrees further than 1,
4, or 5.
It may appear that this division is an arbitrary one, and that
it is difficult to appreciate by figures a phsenomenon like the scin-
tillation of the stars : but this mode of proceeding is indicated
by several learned men ; among others by the celebrated Horace
Benedict de Saussure, who employed a similar means of estima-
ting the famous dry fog of 1783.
De Saussure gives the amount of intensity sometimes as 3,
the {Scintillation of the Stajs. 219
sometimes as 4, and sometimes as 8, &c., and gives the follow-
ing reasons for so doing: — "This scale that I have employed
is an imaginary division for the estimation of a phsenomenon for
which we can have no real measure. I suppose, then, that the
highest degree is 10, the lowest 1; and I shall endeavour to
determine the intermediate degrees either by the intensity of the
sensation produced, or by other circumstances connected with
the phsenomenon. This appears to me to present ideas with
more precision than by simply qualifying the diflferent degrees
by the vague terms of strong, middling, and feeble. Thus I
would estimate at 8 degrees the fog of July 3, 1783." (De Saus-
sure. Travels in the Alps : Third Journey, chap. 2.)
I have explained the scale I employ ; other observers can form
their own, according to their ideas of what is best. The num-
bers can be changed at will, so long as the degrees remain prac-
tically the same. Thus, my brother Mark, who began his ob-
servations about a year ago, has adopted a scale much lower than
mine ; but we always agree as to the amount of scintillation on
any given evening, and also as to whether one star scintillates
more than another. These are the most important points to
decide on ; for, as all the observations cannot be taken by the
same person, it would often be difficult to ascertain if the scin-
tillation is of the same intensity at Cairo, New Archangel, on
the Peak of Tcneriffe, or at Morges.
Within certain limits this difficvdty can be obviated, as I vnW
endeavour to show later; but in any case, by following the
method of instruction I have indicated, it will be possible to
know how much the scintillation varies from one night to an-
other, and whether the amount appears affected or is influenced
by any meteorological perturbations.
It is of course needless to add, that the height of the star ob-
served must be known and noted. It is not necessary, however,
to take a direct observation of the height of the star in question ;
it is much easier to calculate this from the time of the night ;
and, to abridge these calculations, a Table can be drawn up indi-
cating what is the exact height of the stars to be observed in the
different sidereal hours, according to the latitude of the obser-
vei-^s position. The Table I have gives the degrees of height for
Morges, calculated at intervals of half an hour. And this Table
is sufficient; for in the space of half an hour one can interpolate
with all the exactitude necessary, as in this case it is only need-
ful to know approximatively, within a degree or half a degree, the
height of the stars.
2nd. Mode of comparing observations.
It has been proved that, all other circumstances being equal,
the scintillation of the stars decreases in proportion as they ap-
220 Prof. Dufour: Instructions for the better observation of
proach the zenith ; and reasoning fi-om this fact, it may seem
impossible to compare observations unless they have all been
taken from stars at the same height. On comparing a vast
number of observations taken under most favourable conditions,
and when there had been no apparent atmospheric perturbations
either on the preceding or following days, I have placed it beyond
doubt that the scintillation does really decrease when the stars
approach the zenith, and that, for any given height, the scin-
tillation is sensibly proportional to the product obtained by mul-
tiplying the depth of the stratum of air wliich the rays of light
traverse, by the astronomical refraction for the height under con-
sideration.
Let us designate this product by P. Representing by 1
the height of the atmosphere, and estimating the refractions in
seconds, it will be found that for the different heights the results
P are —
Ileight of the star. Value P.
20 444
25 286
30 198
35 143']
40 106-9
45 81-8
50 63-6
55 49-7
60 387
65 30-3
70 22-5
75 16-1
80 10-4
85 5-1
These figures represent tolerably well the normal state of the
scintillation at Merges, when the height of the star above the
horizon varies from 20'^ to 75°. Below 20° the calculated value
no longer corresponds with the observations, but the neighbour-
hood of the horizon sufficiently explains this deviation ; and as
to the stars situated at a height which exceeds 75^, their scintil-
lation is in general so feeble that the slightest error in the ob-
servation will cause a notable modification in the correspondence
of the figm-es. Thus, if one has observed at a height of 60° a
scintillation of l*6j and one wishes to know what would have
been, under the same circumstances, the scintillation of the same
star if it had been only 45" above the horizon, one would obtain
Scintillation at 45°= "^^gg.y^'^ =3-4.
the Scintillation of the Stars. 221
3rd. Errors to he avoided.
It often happens that from one night to another the scintil-
lation varies very considerably ; but it augments or diminishes
proportionably for all the stars, except perhaps for those which,
being nearest the horizon, have always a strong scintillation, or
except when accidental causes modify it momentarily. Among
these accidental causes we may cite, first, the twilight, which
almost always very much augments the scintillation ; and
secondly, the neighbourhood of clouds. I think M. Kaemtz
was the first to notice that the scintillation augments when there
are clouds driven by the wind. This is the fact, as I have ob-
served it in thousands of cases, and I do not remember noticing
a single exception.
Hence I do not say that we ought to reject observations taken
when the stars are near clouds ; only we must bear in mind this
circumstance, as it greatly modifies the results obtained. A
bright moonlight is also very unfavourable; for observations
taken when the moon is full, are much less exact than those
taken when she is absent.
4th. Comparison of the observations made by different persons.
This is the delicate point to consider ; for what precedes suf-
fices for the study of the phsenoraenon when all the observations
are taken by a single person ; but when there are several, how are
we to know if the scintillation designated 2'5 is equal to that
of another person also designated by 2-5 ? I believe it is im-
possible to obtahi this unison ; and unless every observer could
be taught by one single person experienced in the matter, I am
certain it never will be obtained. However, here is a method of
recognizing if the scintillation is, in absolute value, stronger in
one station than in another : —
At Merges, during the nights of maximum scintillation, the
stars at the zenith scintillate very decidedly. In the nights of
middling scintillation the stars in the same position scintillate
feebly, though always enough to be appreciable ; but in the
nights when the scintillation is at its minimum, the stars
nearest the zenith have no longer any scintillation at all ; and
the nearer the scintillation approaches to its minimum, the more
extended is the spherical segment (of which the zenith is always
the centre), which comprehends all those stars of which the
scintillation is inappreciable. I have sometimes seen, when the
scintillation was very feeble, that the stars lost all scintillation
as soon as they were at l^"^ above the horizon ; but I have never
seen it cease entirely for stars less elevated, though, from what
Arago says, it appears that that happens sometimes.
He names, among others, the observations of M. de Hum-
222 Prof. Dufour : Instructions for the betto' observation of
boldt, who says that on the borders of the Orinoco no scintil-
lation can be observed^ not even at 4^ or 5° above the horizon.
Le Gentil asserts that at Pondicherry, during the months of
January and February, the stars do not scintillate at all. Beau-
champ wrote to Lalande, that at Bagdad the stars ceased to
scintillate as soon as they arrived at 45' above the horizon.
Garcin asserted, in 1743, that at Bender Abassi, on the
borders of the Persian Gulf, in the spring, summer, and autumn
the stars did not scintillate; it was only in winter that a slight
scintillation was perceptible.
According to M. de Humboldt, at Curnana in general the
scintillation is no longer sensible when the stars are more than
25° above the horizon, &c. Most assuredly I have never seen
at ]\Iorges, during the past six years, so small an amount of
scintillation ; but it is by specifying the various heights at which
stars cease to scintillate that my observations are susceptible of
being compared with those of M. de Humboldt and Le Gentil.
I therefore call the attention of observers specially to this point,
as probably the best manner of comparing the calculations
obtained in various parts of the globe.
The scintillation of stars of the first magnitude is perfectly
appreciable by the naked eye ; that of the secondary ones less
so; and so on, until for the smallest and least brilliant stars it
becomes quite inappreciable : but this limit varies from one
night to another, according as the general scintillation is strong
or feeble. This fact may also serve as a means of comparing
the degrees of scintillation.
The magnitude of the stars that appear to scintillate must be
noted ; and as we have seen that the height of the stars above
the horizon exercises a great influence on the intensity of the
phsenomenou, it will be necessar}'' to name some of the stars,
and to indicate, besides, their height above the horizon, or at
least the time at which the obsen'ation was taken ; but I attach
less importance to this method of comparison than to the pre-
ceding one, because the purity of the atmosphere, the sight of
the observer, and the various degrees in the brilliancy of the
stars, all exert more or less influence on the results obtained.
5th. Variable Stars.
Of all the stars I have observed, a. of Orion is the one of which
the scintillation appears to me to be the most irregular ; but it
is well known that the brilliancy of this star is not always the
same : and with reference to the variable stars, all that is known
of them is the duration of their periods ; and consequently their
scintillation is also an interesting phsenomenon to study. It would
be, above all, interesting in the case of the star i) of Argo, whose
the Scintillation of the Stars. 223
singular variations of brilliancy have so much surprised astrono-
mers for the last thirty or forty years. Unfortunately this star
is only visible at 31° north latitude ; and to observe it at a height
of 30° above the horizon, one must travel as far as the equator,
so that this research must be left to the astronomers of the other
hemisphere.
6th. Scintillation of the Planets.
It is generally believed that the planets do not scintillate at
all, or scarcely at all. Nevertheless I have often observed a
sensible scintillation of Venus and jMars, and in a few rare cases
I have also observed a slight scintillation of Jupiter and Saturn.
For those persons who undertake to explain the pha?nomenon of
the scintillation, it would be important to know if really the
scintillation of these planets ever becomes very decided.
I would therefore call the attention of observers who may find
themselves under atmospherical conditions of a nature to render
the general scintillation very strong, to this point, as they might
perhaps be able to ascertain whether Jupiter and Saturn ever
sensibly scintillate.
7th. Accidental Observations.
In order to complete the study of this phsenomenon, excep-
tional circumstances must not be neglected : — Among others,
observations taken during an aurora borealis, both of the stars
which appear plunged in the light of the aurora, and of the
others in other parts of the heavens. During six years I have
never been able to make any observations of this nature at
Morges.
The observation of the scintillation from the summit of a high
mountain. De Saussure made several during the time he was
on the "Col du Geaut j^^ but those which are given in the works
of this celebrated man are too few in number, and not detailed
sufficiently to be able to draw from them any certain conclusions.
Mr. Piazzi Smyth remembers that the scintillation appeared
to him very feeble from the summit of the Peak of TenerifFe ;
and during the time I was staying on the Great St. Bernard,
I remarked that the general scintillation was always very feeble.
Is this always the case ?
8th. Accessor^/ Observations.
In order to render the observations on the scintillation really
interesting and useful, it is important that they should be accom-
panied by meteorological observations as complete as possible.
At least let the state of the barometer, hygrometer, and thermo-
meter be noted exactly ; also the state of the heavens, and the
force and direction of the wind.
224 Royal Society : —
It is probable that vvhcrevev any observations are taken,
meteorological observations arc also taken and published ; so that
it would not be adding materially to the work of observers of the
scintillation to ask them to add those observations to their own.
There are many more details w'hich I pass over, because they
depend on the peculiarity of the sight of different observers, and
on the circumstances inider which they may be placed, and
which of course vary in every individual case : I have contented
myself with indicating the principal points, to which I call the
attention of observers, and the importance of which I know by
experience.
In concluding, let me be permitted to express a w'ish, addressed
to all who may be disposed to observe the scintillation of the
stars in countries whose climates are different to that of Morges ;
and that is, that they w^ould kindly communicate to me a brief
summary of their work — for it is needless for me to say that any
result that they may arrive at will be of the highest interest to
me ; and reciprocally, if they desire it, I shall have great jileasure
in giving any further details or directions to any persons who
will interest themselves in this research.
Morges, December 1859.
XXX. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Continued from p. 158.]
May 20, 1859. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.
THE following communication was read : —
" On the Laws of Operation, and the Svstematization of Ma-
thematics." By Alexander J. Ellis, Esq., B.A., F.C.P.S.
The object of the following investigation is to give a firmer basis
to the calculus of operations, to assign the strict limits and con-
nexion of the mathematical sciences, and to found them upon purely
inductive considerations, without any metaphysical or a priori
reasoning.
Starting with the indemonstrable but verifiable hypothesis, that
objects exist external to the subject, we recognize equality as exist-
ing between objects with common and peculiar properties, in respect
of their common properties. Operations, which, when performed on
equal objects, produce equal objects as their result, are recognized as
equal, in respect to the common properties considered in the equali-
ties of the objects. "When one operation is performed on an object,
and another on the resultant object, the single operation by which the
first object is transformable into the last is regarded as the 2^''oduct
of the other two, the order of succession being important. When
the resultant object is the same as the original operand, the product
of the operations is termed unity. When two operations performed
Mr. A. J. Ellis on the Systematization of Mathematics. 225
on the same object produce different resultant objects, the operation
of transforming one of these resultant objects into the other, is re-
garded as the quotient of the two former operations. Two opera-
tions are termed reciprocal when their product is unity. Ilence the
quotient of two operations is the product of the one and of the reci-
procal of the other. When two objects are combined in any manner
so as to produce a third, and the two first are forinable from any
fourth by two known operations, the single operation by which the
third object can be also formed from the fourth, is termed the same
combination of the two first operations. From this we gain the con-
ception of null or zero, as the operation of annihilating any object in
respect to any place. The product of a combination of two opera-
tions and a third operation, is the same combination of the products
of each of the combined operations severally and the third operation,
in the particidar order thus specified, provided all the operations and
products are performable on the same operand.
The above general conceptions and laws of combined operations
hold for any operations whatsoever with their appropriate operand
objects ; but the nature of the operations and operands requires
especial study. In mathematics, objects are only considered with
respect to their three most general properties : first, as contem-
platable in discontinuous succession, whence number and Arithmetics^
secondly, as contemplatable in continuous succession, whence ex-
tension and Geometry ; and thirdly, as contemplatable in a con-
tinuous succession bearing a relation to another continuous succession,
whence motion in time and Mechanics. The problem of mathe-
matics is, first, to discover the laws of these successions as respects
results (that is, statically), by means of considerations drawn from
contemplating operations (that is, dynamical) ; secondly, to investi-
gate the relations of these laws, giving rise to statical algebra ;
thirdly, to reduce all dynamical to statical laws, as in dynamical
algebra ; and fourthly, to make the expression of all the results de-
pendent on the most simple, viz. those of common arithmetic. The
purpose of the problem is to prepare the mind for the further investi-
gation of nature, and to increase practical power immediately.
In Arithmetic we conceive objects spread out in a scale, and by
aggregating those contained between any one and the beginning of
the scale, form statical groups, whose distinctive character is derived
from the scale. The operation by which any group is formed from
the first object is termed an integer, the especial laws of which are
next investigated. All objects being interchangeable in respect to
discontinuous succession, an aggregate is not changed by altering the
disposition of its parts. This leads to the first two laws of commu-
tation and association in addition. The possibility of arranging
objects at once in two horizontal directions, and a third vertical
direction, leads to the laws of commutation and association in multi-
plication. Combining these with the two former, we have the law
of commutative distribution. From the laws of associ.ition in multi-
pUcation is immediately deduced the laio of repetition or indices.
Ilaving obtamed these laws, we proceed to study their relatious in
226 Royal Society : —
the algebra of integers, first, statically, in order to reduce all results
to the form of a numerical integer ; secondly, dynamically, con-
sidering the effect of a variation in the integer employed. This
leads to the conception of a forynation (Lagrange's "analytical
function"), as a combination of a fixed and independently variable
integer. Such a combination is, therefore, also itself dependently
variable. The inversion of formations, whereby the independent
variable is expressed as a formation of the dependent variable, imme-
diately engages our attention. The inversion of a sum leads to a
difference, with the limitation that the minuend should be greater
than the subtrahend. The inversion of a product leads to a quo-
tient, with the limitation that the dividend should be a multiple of
the divisor. The inversions of a power lead to the root and loga-
rithm, with increasing limitations. The study of discontinuous ob-
jects then allows the application of these inversions to the solution
of problems in common life.
The operation by which any group in the arithmetical scale already
described is formable from any other group in the same scale, leads
to the conception of % fraction, necessarily expressible, according to
the general laws of operation, as the quotient of two integers. The
operands of such operations must admit of being separated into
certain numbers of equal parts, or rather, in order that they may
admit of any fractional operation, into any number of equal parts.
Thus discontinuous approaches continuous succession. The laws of
fractions are the same as the laws of integers, provided the indices
used are all integers. The object of the statical algebra of fractions
is to reduce all combinations of numerical fractions to numerical
fractions. The inversion of formations is less limLed than before.
There is the same limitation respecting differences, but none respect-
ing quotients. The attempt to convert all fractions into radical
fractions (whose denominators are some powers of the radix of the
system of numeration), leads to the conception of convergent infinite
series, and hence allows an approximation to the inversion of a power
with a constant index.
In Geometry, the notion of continuous succession or extension is
derived from the motion of the hand, which recognizes separable but
not separated parts. This motion gives the conception of surfaces,
which by their intersections two and two, or three and three, give
lines and points. Recognizing a line as the simplest form of exten-
sion, we distinguish the straight lines, which coincide when rotated
about two common points, from the curves, which do not. These
straight lines are shown to be fit operands for the integer and fraction
operations. By moving one coinciding line over another so as to
continue to coincide (by sliding), or to have one point only in com-
mon (by rotating), or no points in common (by translation), we
obtain the conceptions of angles and parallels, which suffice to show
that the exterior angle of a triangle is equal to the two interior and
opposite, and that two straight lines meet or not according as the
exterior angle they make with a third is not or is equal to, the
interior angle. Angles are then considered statically as amounts of
Mr. A. J. Ellis on the Systematization of Mathematics. 227
rotation not exceeding a semi-revolution. Proceeding to examine
the relations of triangles and parallelograms, we discover the opera-
tion of taking a fraction of a straight line, and therefore of a triangle
and of any rectilineiil figure. We see that this operation is, in fact,
the same as that of altering a third line into a fourth, so that the
multiples of the third and fourth, when arranged in order of magni-
tude, should lie in the same order as those of the first and second
when similarly arranged. The relation of two magnitudes, with
respect to this order, we term their ratio, and the equality of ratios
•proportion. The inversion and alternation of the four terms of a
proportion are now investigated. The operation of changing any
magnitude into one which bears a given ratio to it, is called a tensor.
The laws of tensors, being investigated, are shown to be the same as
those of fractions. They, however, furnish the complete conception
of infinite and infinitesimal tensors, by letting one or other of the mag-
nitudes by which the ratio is given become infinite or infinitesimal.
Thence is developed the law, that tensors differing infinitesimally are
equal for all assignables. Consequently tensors may be represented
by convergent series of fractions. The algebra of tensors allows of
the inversion of a sum with the same limitation as in the case of
fractions, the complete inversion of a product of tensors, and the
practical inversion of a power with a constant integral index. This
algebra applied to geometry allows of the investigation of all statical
relations, that is, of all the geometry of the ancients, in which
magnitudes alone were considered, without direction. In respect to
areas, the consideration of the parallelogram swept out by one straight
line translated so as to keep one point on another straight line, leads
to an independent algebra of areas, in which the generating lines are
considered immediately. The laws of the relations of lines thus
discovered, are shown to be identical with the laws of the relations
of tensors. Consequently, with certain limitations, the whole of the
algebra of tensors may be interpreted as results in the algebra of
areas. This leads to a perfect conception of the principle of homo-
nomy, or dissimilar operations having the same laws, and conse-
quently the same algebra.
In dynamical or modern geometry, all lines are considered as in
construction, having initial and final points. If the initial points of
any two straight lines are joined to a third, not on either, and the two
parallelograms be completed, the linos diawn from the point parallel
to the given lines are dynamically equal to them ; if these last
lie on each other, the first two lines have the same direction ; if the
last have only one point in common and lie in the same straight line,
the first have opjwsite directions ; and if the last do not lie in the
same straight line, the first have different directions, and the angle
between the last is the angle between the first lines. Similar defini-
tions can be given of direction in the case of angles and circular
arcs. If from the final point of any line we draw a line equal to
a second, and join the initial jiohit of the first with the final point
of the line thus drawn, we are said to append the second to the first,
and the joining line is called the appense of the other two. The
228 Royal Societij .—
laivs of appe)ision are shown to be the same as those of addition,
and are hence expressible by the same signs of combination, the
difference in the objects combined preventing any ambiguity. We
thus get the conception of a point as an annihilated line.
The tensor operation, considered dynamically, leads to the opera-
tion of changing a line dynamically so that it should bear the same
relation to the result as two given lines bear to each other in magni-
tude and direction. This assumes three principal forms according
to the diflference of direction. If there is no diiference of direction,
the operation is purely a tensor. If the directions differ by a semi-
revolution, the rotation of one line into the position of the other may
take place on any plane. The operation is then termed a negative
scalar ; the tensor, which includes the operation of turning through
any number of revolutions, is distinguished as a positive scalar. If
the rotation be through any angle, but always on the same plane,
the operation is here termed a clinant. If the rotation may take
place on any variable plane, the operation is a quaternion.
The laios of scahn-s are immediately proved to be the same as
those of tensors, but in addition they introduce the idea of negativity.
This enables us in the ahjehra of scalars, to invert a sum generally,
and thus allows of a perfect inversion of the first two formations.
But a power with a fixed integral exponent can only be inverted on
certain conditions. This partial inversion, however, leads to a solu-
tion of quadratic equations, and to a proof that formations consisting
of a sum of integral powers, cannot be reduced to null by more
scalar values of the variable than are marked by its highest exponent.
Hence if such a formation is always equal to null, all the coefficients
of the variable must be null. We thus obtain the method of inde-
terminate coefficients, by which we are enabled to discover a series
which obeys the laws of repetition with respect to its variable, and
becomes equal to a power Avhen its variable is an integer. This
enables us to define a power with any index, as this series, and hence
to attempt the inversion of powers with variable indices, which we
succeed in accomplishing under certain conditions. This investigation
introduces the logarithm of a tensor, powers with fractional and
negative exponents, and the binomial theorem for these powers. It
also induces us to consider the laivs offormators, or the operations
by which a formation of any variable is constructed. They are
shown to be commutative and associative in addition, associative in
multiplication, directly distributive and repetitive, but not generally
commutative in multiplication, nor even inversely distributive. When
formators are commutative in multiplication and distribution, they
are entirely homonomous with scalars, which may even be considered
as a species of formators. The results of the former investigation,
therefore, show that logarithms, fractional and negative powers, and
the binomial theorem hold for these commutative formators.
The necessity of tabulating logarithms and of approximating to
the solutions of equations, leads to the consideration of a method of
deriving consecutive values of formations for known differences of
the variable, and of interpolating values of the same formation for
Mr. A. J. Ellis on the Systematization of Mathematics. 229
intermediate values of the variable ; that is, the algebra of differences.
Considering the two operations of altering a formation by increasing
the variable, and taking the difference between two different values
of the formation (of which operations the first is necessarily unity
added to the second), we regard them as formators, and immediately
apply the results of that algebra, which furnishes all the necessary
formulae. For approximating to the roots of equations, we require
to consider the case where the variable changes infinitesimally, thus
founding the algebra of differeyitials, which is, in fact, a mere sim-
plification of that of differences, owing to all the results being ulti-
mately calculated for assiguables only. Finally, to find the alteration
in a formation of commutative formators, when the variable formator
is increased by any other foimator, we found the algebra of deri-
vatives.
In applying the results oi scalar algebra to geometry, we start with
the fundamental propositions that the appense of the sides of an en-
closed figure taken in order is a jioint, and that when the magnitude
and direction of the diagonal of a parallelogram or ])arallelopii)edon,
and lines parallel the sides which have the same initial point as the
diagonal, are given, the whole figures are completely determined. In
order to introduce scalars, a unit-sphere is imagined, with its radii
parallel to the lines in any figure, and in known directions. Any line
can then be represented as the result of performing a scalar operation
on the corresponding radius.
The first object is to reduce the consideration of angles to that of
straight lines, by the introduction of cosines and sines, which are
strictly defined as the scalars represented by the relation of the
abscissa to the abscissal radius, and the ordinate to the ordinate
radius respectively. These definitions immediately lead to the rela-
tions between the cosines and sines of the sums of two angles, and
those of the angles themselves, whatever be their magnitude or direc-
tion, and thus found goniometry.
Defining a projection of any figure on any plane to be that formed
by joining the points on that plane corresponding according to any
law with those of the figure, we have the fundamental relation that,
if the first, and therefore the second figure is enclosed, the appense of
the sides of the second in the order indicated by the sides of the first,
is a point. The orthogonal projection of any figure, by means of
planes drawn perpendicular to any line, being all in one line, each
projection can be represented as the result of a scalar operation per-
formed on the same unit radius, and hence this projection leads to one
invariable relation between scalars. By choosing three lines at right
angles to each other on which to j)roject, we obtain three scalar re-
lations from every solid figure. If the figure is plane, then by pro-
jecting on a line and on a perpendicular to that line, we get two
scalar relations.
Applying these results to transversals, where a line parallel to one
unit radius cuts several other unit radii, produced either way if neces-
sarv, we obtain, by considering two intersected radii, the results of
Phil. Mag. S. 4. Vol. 19. No. 126. Mar. 18G0. R
230 Royal Society : —
trigonometry, and by coBsidering three or four intersected radii,
those of anharmonic ratios.
As any line drawn from the centre of the unit-sphere may he con-
sidered as the appense of three hnes draxMi along or parallel to three
given unit radii, it may he expressed as the sum of the results of
three scalar operations performed on these radii respectively. By
properly varying these three scalars, the final point of the line may
be made to coincide with any point in space. But if there be a given
relation between the scalars, then the numher of points will be
limited, and the whole number of the points constitutes the locus of
the original concrete equation referred to the accessory abstract equa-
tion. The consideration of this entirely new view of coordinate geO'
iiietry is reserved for a second memoir.
Proceeding next to the lans of dinants, we readily demonstrate
thai they are the same as the laws of scalars ; they introduce a new
conception, however, that of rotating through an angle not necessarily
the same as a semi-revolution, that is, of a plane versor. By the con-
crete equation of coordinate geometry, it is immediately shown that
all clinants can be expressed as the sum of a scalar, and of the pro-
duct of a scalar by a fixed, but arbitrarily chosen versor. The
simplest versor to select is the quadrantal versor, which, under the
name of qtiadrantatiou, is now studied. The two addends ofaclinant,
considered as a sum, are called its scalar and vector ; its two factors,
considered as a product, are its tensor and versor. The laws of these
parts are then studied.
The statical algebra of dinants has for its object the reduction of
all combinations of clinants given in the standard form of the sum of
a scalar and vector, to a clinant of the same form. The application
of this to the series obtained for a general scalar power, leads to two
series, called cosmes and sines of the variables, as distinguished from
the goniometrical cosines and smes of an angle, with which they are
ultimately shown to have a close connexion, which can be rendered
most evident by assuming as the unit-angle that subtended by a cir-
cular arc of the length of its radius. Studying these series quite in-
dependently of these relations to angles, we discover that they bear to
each other the same relations as the goniometrical cosines and sines,
and that if the least tensor value of the variable for which the cosine
series becomes null, is known, all' its other values can be found by
multiplying this by four times any scalar integer. This last product
must be added to the least tensor value of the variable for which
both the cosine or the sine series become equal to given scalars, in
order to find all the solutions of such equations. Supposing the
values of such series tabulated by the method of differences for all
scalar values of the variable, so that such least tensor values can
always be found, we are now able to assign the meaning of any
power whose base and index are both clinants, and the logarithm of
any cUnant. This enables us to invert completely all the simple for-
mations, sum, product, power with variable base and constant index,
or constant base and variable index ; and hence to solve all equations
Mr. A. J. Ellis on the Sysiematization of Mathematics. 231
of four dimensions with clinant coefficients, and to sliow that every
formation consisting of a sum of integral powers with clinant coeffi-
cients, can be expressed as a j)roduct of as many simple formations as
is determined by the highest index of the variable. The cosine and
sine series can also be generally inverted. The versor of any clinant
having a known angle (which is always equal to the cosine of its
angle added to the product of the sine of its angle into a quadrantal
versor), can now be shown to equal the cosine series added to the sine
series multiplied by a quadrantal versor, when the variable of the
series is the scalar ratio of the angle of the clinant to the angle sub-
tended by a circular arc equal to its radius. From this the ratio of
the circumference to the diameter of a circle is shown to be t'nice the
least tensor value of the variable, for which the cosine series is equal
to null ; and as that value can be readily assigned in a convergent
series, the former ratio is determined. The same investigation shows
the relation already mentioned between the gouiometrical cosines
and sines, and the cosine and sine series.
Clinant aJyehraical yeometrxj allows us to interpret all results of
clinant algebra when referred to lines on one plane. It thus fur-
nishes a complete explanation of the " imaginary" points and lines
in the theory of anharmonic ratios, when viewed in relation to the
unit radii, as already explained. In the case of coordinate geo-
metry of two, and even three dimensions, the possibility of interpret-
ing the results of a clinant operation performed on a given unit radius
in a given plane, allows us to understand the whole theory of " ima-
ginary " intersections. The theory of scalar and clinant alyebraical
coordinate geometry will form the subject of a future memoir.
Proceeding to quaternions, we find their laws to be the same as
those of clinants while the plane remains unaltered ; but if the plane
is alterable, they cease to be commutative in multiplication, that re-
lation being replaced by one between certain related quaternions
called their conjugates. This makes the algebra of quaternions
(which is not here systematized, as being too recent) entirely different
from that of scalars.
In 7nef)hanics the motion of any point is not considered absolutely
as in dynamical geometry, but relatively to some external, constant,
independent motion, as the apparent motion of the fixed stars ; this
gives the conception of time. But the necessity of considering the
motion not merely of a point, but of a body, gives rise to the com-
parison of the motions of varigps bodies, and to a conception of their
equality, when the products of their velocities, multiplied by a con-
stant which is always the same for the same body, but difi'erent for
different bodies, are equal. This constant is the mass, which in
bodies of the same kind varies as the volume.
By considering the case of the mutual destruction of motion, we
eliminate time and simplify the problem, thus fouuding statics ;
and by conceiving the motion of any body to be destroyed by the
application of variable motions equal and opposite to those actually
existent, we reduce dynamics to statics.
R2
232 Royal Suciety : —
Nov. 17, ISaO. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.
The following conimiuiication was read : —
" Notes of Researches on the Poly-Ammonias." — No. VI. New
Derivatives of Phcnvlamine and Ethylamine. By A. W. Ilofmann,
LL.D., F.R.S. &c.'
Some time ago* I communicated to the Royal Society some re-
sults ohtained in studying the action of dibromide of ethylene upon
phenylamine. The principal product of this reaction was found to
be a well-defined crystalline compound with basic characters. By
the analysis of the base itself, and of several of its combinations, it
had been proved that the formula
n -a fj— (C4 H J" ] XT
is the simplest atomic expression for the new substance ; but the
action of iodide of methyle and of ethyle upon this body having given
rise to compounds
C3.H,,N,I=:^-|^5J}c.H3l
and
CTT XT T '-^le ■t'l -"^ I P TT T
36 ■'^as-'^^a ^ — Q JJ >^T r '-'^ AI5 1,
I was induced to assume the formula
as representing the true constitution of the basic body, which thus
appears as a diammonia, in which 2 cquivs. of hydrogen are replaced
by 2 equivs. of phenyle, audi equivs. of hydrogen by 2 molecules of
diatomic ethylene.
This view involves the existence of a basic compound,
a,H,,N,=(C,,H3)jN„
H.
1
i.e. of a diphenyl-diamine in which only one molecule of diatomic
ethylene has been substituted for hydrogen.
Experiment has not failed to realize the body pointed out by
theory. A mixture of dibromide of ethylene with a large excess of
phenylamine (1 vol. of dibromide of ethylene and 4 vols, of phenyl-
amine) rapidly solidifies to a crystalline mass. Treatment with
water removes from this mixture a very considerable proportion of
hydrochlorate of phenylamine, leaving a brown resinous substance,
which gradually but imperfectly solidifies. This substance forms a
hydrochlorate which is difficultly soluble in concentrated hydro-
chloric acid, and which may be readily ])urified by repeated crystal-
lizations from boiling alcohol. The ])ure hydrochlorate dissolved
in water, and mixed with potassa or ammonia, furnishes the free base,
which generally separates as an oil, rapidly solidifying into a cry-
* Phil. Mag, vol. xvii. p. 66.
T)r. Hofmann on Derivatives of Phenylumine and Ethijlamine. 233
stalline substance. This may be further puritied by repeated crystal-
lizations from diluted alcohol.
Analysis, in fact, assigns to this body the formula
C,,n„N,= (C,,H,)., !-N..
' PI , "
which was confirmed by the analysis of the dichloride —
Cl„
(C,II,)"
H.
t J J
and of the platinum-salt —
(C.II,)"
(C.H,)4N,
H,
CI, 2 Ft CI,.
The formation of the new body is obvious :
(C,H,)"
4[^'={J^}N]-f(C,HJ'Br, = (C:,IU N.,-f2(^[^-J|^}N]Br^
Phenylamine.
Dibromide of
E hylene.
Ethylene-
diplieiiyl-
dianiiue.
Bromide of
Phenvl-aramoniuui.
This substance differs in its physical characters essentially from
the base containing 2 molecules of ethylene. The former is very
soluble in alcohol and ether, the latter being very difficultly soluble ;
its fusing-polnt is 59°, the fusing-point of the latter being 1.5/°.
In order finally to establish the relation between the body which
forms the subject of this note and the base previously described, it
remained to prove experimentally that the former, when submitted
to the action of dibromide of ethylene, may be readily converted into
the latter. Nothing is easier than to accomplish this transforma-
tion, which, in the presence of alcohol, is rapidly effected at the
temperature of boiling water.
Treatment of the product of digestion with water removes the
dichloride of ethylene-dii)licnyl-diammonium, the diethylene-diphe-
nylamine remaining dissolved in the excess of dibromide of ethylene,
from which it may be readily extracted by hydrochloric acid.
Preparation of the substance in a state of purity, and com})arison
of its properties with those of the body previously obtained, esta-
blished beyond a doubt the transformation, which resolves itself into
a simple process of substitution —
(C,II.)"
(C„n,).
H,
N.,
+ (C.HJ"13r, = ™^}
+ N
(c.ii.r
II.
N.,
Br.
234.
Royal Society.
Ethylene-dipheuyl-diamiue being a secondary diamine, it was not
Avithont interest to replace tlie two remaining hydrogen-equivalents
by two nionatomic molecules. On digesting the base with iodide of
ethyle sonic Isours at a temperature of 100°, a beautiful iodide was
obtained, crystallizing in well-defined prisms, difficultly soluble iu
water, but more soluble in alcohol.
This substance contains
C3,H3,NJ,=
r(C,HJ"
(C,H,), . ..
Treatment with potassa separates from this iodide the base as a
crystalline body fusing at 70°, and resembling in many respects the
previous base. It contains
N„
and forms a beautiful platinum-salt crystallizing in needles of the
formula
[C33H,eNJ"Cl„2PtCl,.
The deportment of phenylamine under the influence of dibromide
of ethylene gives a fair illustration of the nature of the substances
which are generated, under the influence of diatomic molecules, from
primary aromatic monamines.
To complete the study of this subject, I have examined, moreover,
the action of dibromide of ethylene upon ethylamine, as a repre-
sentative of the monamines containing an ordinary alcohol-radical.
Dibromide of ethylene acts upon ethylamine even in the cold, the
products of the reaction varying according to the relative proportions
of the two bodies, and according to the temperature. Among other
products invariably occur the two bromides corresponding to the
two salts of the phenyl-compouuds mentioned in the previous para-
graphs.
These substances are the
Dibromide of
ethylene-diethyl-
diammonium,
Dibromide of
diethylene-dietbyl-
dianimonium,
C„H„N,Br,=
C,,H,,N,Br.=
-(C,HJ"
(C,H,),
N,. Br, and
N.. Br.-,
I have fixed the composition of the former compound by the ana-
lysis of the dibromide of the dichloride and of the base itself, all of
which are remarkably well-defined crystalline bodies, and that of
the latter by the examination of a well-defined platinum-salt.
G 'ological Society. 235
The first base, separated by the action of anhydrous baryta from
the drv bromide, distils as an oily liquid of a powerfully ammoniacal
odour, which solidifies into a brittle crystalline mass not unlike
fused stearic acid. The composition of the body is remarkable.
It contains
and thus constitutes the dioxide of the diatomic metal, ethylene-
diethyl-diammonium.
The second base is liquid, and boils at 185°. It is easily obtained
from the dibromide, which, being extremely soluble, may be readily
separated from the bromide of the first body. I have experimentally
established that this body may be readily procured by the action of
dibromide of ethylene upon the dioxide previously mentioned.
The dioxide,
presents considerable interest in a theoretical point of view. I have
determined the vapour-density of this compound by Gay-Lussac's
process. Experiment gave the number 2'26. Assuming that the
molecule of the body under examination corresponds to 4 volumes
of vapour, the theoretical density is 4'62.
The extraordinary discrepancy between theory and experim.ent
may be removed in two ways : viz. either by halving the formula,
or by assuming that the molecule of the dioxide of ethylcne-diethyl-
diammoninm corresponds to 8 volumes of vapour, in either of which
cases the theoretical density becomes '2-31, closely agreeing with the
experimental number 2*2G.
I shall discuss the vapour-densities of the diammonias somewhat
more fully in a future communication ; but I cannot refrain from
pointing out even now, that, by dividing the formula by 2, we arrive
at an expression containing 1 equiv. of oxygen (0=8), which, in the
eyes of those who consider the number 16 as the true molecular
value of oxygen, must appear perfectly inadmissible.
GEOLOGICAL SOCIETY.
[Continued from p. 162.]
January 18, 1860. — Sir C. Lyell, Vice-President, in the Chair.
The following communications were read : —
1. "Notice of some Sections of the Strata near Oxford." By
John Phillips, M.A., LL.D., F.R.S., Pros. G.S. &c.
From the Yorkshire coast to that of Dorset, evidence of uncon-
formity between the OoUtic and the Cretaceous strata is readily-
observed, the latter resting on several different members of the
former along this tract. This is especially seen in the neighbour-
236 Geological Society : —
hood of Oxford, where it is difficult to trace out correctly the limits
of the Lower Cretaceous beds. The Oolitic rocks having been
deposited whilst the relative position of the land and sea was being
changed, many of tlie deposits are subject to local limitation ; thus
the Coralline, Oolitic, and tlie Calc-grit die out rapidly, and the
Kimmeridge Clay comes to rest on the Oxford Clay. It is on the
surface formed by these irregular beds, and that surface considerably
denuded, owing to elevations before the Oolitic period was ended,
that the Lower Cretaceous beds have been laid down. From their
close propinquity, the sand-beds of different ages, when without
fossils, are scarcely to be defined as Oolitic or Cretaceous, and where
one clay lies upon a similar clay, the occurrence of fossils only can
secure their distinction.
The Farringdon sands, the sands of Shotover Hill, and those near
Aylesbury, are still open to research, — their Lower Greensand
characters not having been clearly established. At Culham, a few
miles south of Oxford, u clay-pit is worked, which presents, at the
top, 3 feet of gravel ; next about 20 feet of Gault with its peculiar
fossils ; then 9 feet of greenish sand, with a few fossils ; and lastly
23 feet of Kimmeridge Clay, with its peculiar Ammonites and other
fossils. In winter the clay-pit, being wet, offers little evidence of
any distinction between the upper and the lower parts of the clay ;
but in summer the Gault and its fossils are more easily recognized.
The intervening sand contains Thracia depressa, Cardium striatulum,
and an Ammonite resembling one found in the Kimmeridge Clay.
Although this sand at first sight resembles the Lower Greensand,
yet it is probably more closely related to the Kimmeridge Clay.
Puzzling as this sand is in the ])it, another enigma is offered
by the railway-section at Culham, where the Kimmeridge Clay
is overlaid by a sand perhaps equivalent to that of Shotover
Hill, not that of the clay-pit ; whilst the Gault, which lies on it
unconforraably, can be connected with that of the clay-pit. At
Toot Baldon also, though Lower Greensand jirobably caps the hill,
yet an Oolitic Ammonite was found on the eastward slope of the
hill, in a ferruginous sand, lying conformably on the Kimmeridge
Clay. From these and other instances the difficult}^ of mapping the
country geologically may be shown to be very great, — the sands of
any one bed differing in colour from green to red, according to the
amount of oxidation produced by exposure and other causes ; and if
fossils are absent, the Portland Sand and the Lower Greensand,
lying against each other, may never be defined. From the great
and irregular denudation, too, of the rocks, and the unequal de])o-
sition of many of the beds, it will prove a difficult problem to trace
the several sands and define their age, — a problem to be solved only
by close perseverance and strict search for organic remains.
2. " On the Association of the Lower Members of the Old Red
Sandstone and tlie Metamorjihic Rocks on the Southern Margin of
the Gramjiians." By Prof. R. Ilarkncss, F.R.S., F.G.S.
The area to which this paper referred is the tract lying between
On the Old Red Sandstone of the South of Scotland. 237
Stonehaven and Strathearn, including the south-eastern flanks of
the Grampians for about two-thirds of their course. Alctamorphic
rocks, trap-rocks, the Lower and Middle members of the Old Red
{Series (the former being sandstone, and the latter conglomerate),
are the constituent rock-masses of the district, and give it its pecu-
liar physical features. Tlie mode in which these rocks are associated
is well exhibited in the section on the coast (at Stonehaven), and in
the several sections in the interior where streams lay bare the rocks.
Sections at Stonehaven, Glcnburnie, Strathfinlass, North Esk, West
Water of Lithnot, Cruick Water, South Esk and Prosen, Blairgowrie,
Dunkeld, Strathearn, and Glenartney, were described in detail.
Against the nearly vertical, but somewhat north-w'esterly dipping,
metamorphic schists (which sometimes include conformable lime-
stones), come purple flagstone, but usually separated from them by
trap-rocks, having the same strike. These flagstones pitch to the
south-east, but retain a high angle away from the schists, and, in
many places, are intercalated with beds of trap. The lower purple
flagstones are unfossiliferous ; but higher up tracks of Crustaceans
(Protichni(es) have been discovered by the Rev. H. Mitchell. The
grey fossiliferous flagstones of Forfarshire succeed, still with a steep
dip. Conglomerates succeed, in beds having a less inclination,
gradually becoming more and more horizontal as they reach the low
country.
The axis of the elevation of the Grampians thus appears to be
along their southern margin, and to be marked by the trap-rocks
separating the metamorphic schists and the purple flagstones of the
Old Red series, and giving the latter their general south-easterly
dip. As the metamorphic rocks of the Grampians have not yielded
any fossils, their relation to the other old rocks of Scotland is diffi-
cult to determine.
3. " On the Old Red Sandstone of the South of Scotland." By
Archibald Geikie, Esq., F.G.S., of the Geological Survey of Great
Britain.
This paper was the result of a series of explorations carried on at
intervals from Girvan to St. Abb's Head. The first part related to
the geology of the border-district of Lanark and Ayr, near Lesraa-
hagow. The Silurians and Lower Old Red sandstones of that
district, as formerly pointed out by Sir Roderick Murchison, form
one consecutive series. They are traversed by great numbers of
felstone-dykes, and are disposed in longitudinal folds, ranging from
N.E. to S.W., the Silurian strata forming the axis of each anticline.
Both series are overlaid unconformably by Carboniferous strata
belonging to the horizon of the Moimtain Limestone group of
Scotland. The features of this unconformitj' are well displayed all
round Lesmahagow, where an enormous series of Lower Old Red
sandstones, more than 10,01)0 feet thick, have their truncated edges
overlapped by gently inclined beds of Carboniferous sandstone, shale,
and limestone. The whole of the Lower Carboniferous group and
the upper Old Red Sandstone, amounting in all to at least 6000 or
238 Royal Institution : —
8000 feet, are here wanting. But as the junction of the Carboni-
ferous Limestone with the Lower Old Red is traced towards the east,
the thickness of strata between the two formations gradually in-
creases, until at the Pentland Hills the whole of the Lower Carboni-
ferous series and a considerable part of the L^pper Old Red have come
in ; and these strata, as at Lesmahagow, rest quite unconformably on
the base of the Lower Old Red Sandstone and the higher beds of
the L'pper Silurian. Hence it becomes apparent that in the south
of Scotland, as in Ireland, there is a great physical break between
the Upper Old Red Sandstone and the lower part of that for-
mation.
The author next pointed out the character of the Upper Old Red
Sandstone in East Lothian and Berwickshire ; showing that it
graduated by imperceptible stages into the Lower Carboniferous
sandstones, and formed with these one great lithological series.
The former wide extension of the Upper Old Red Sandstone
throughout the south-east of Scotland w^as shown by the height at
which it occurs among the Lammermuirs. These hills must un-
questionably have been covered by it ; and hence the denudation of
the south of Scotland will eventually be shown to be one of the greatest
which this country has undergone. The author concluded by
sketching the physical geography of South Scotland during the
L'pper Old Red Sandstone period, in so far as it was indicated by
the facts presented in this paper. He showed that the rate of
subsidence was probably much greater in the eastern than in the
western districts, inasmuch as the whole of the vast series of L^pper
Old Red and Lower Carboniferous sandstones had accumulated in
the Lothians and Berwickshire before the base of the Lesmahagow
hills beffan to be washed bv the v.aves of the encroaching sea.
ROYAL IXSTITUTIOX OF GREAT BRITAIX.
January 20, 1860. — " On the Influence of Magnetic Force on the
Electric Discharge." By John I'yndall, Esq., F.R.S.
The intention of the speaker was to bring before the meeting a
series of experiments illustrative of the constitution of the electric
discharge and of the action of magnetism upon it. The substance
of the discourse was derived from the researches of various philo-
sophers, its form being regulated to suit the requirements of the
audience.
1. The influence of the transport of particles was first shown by
an experiment suggested, it was believed, by Sir John Herschel, and
performed by Professor Daniell. The carbon terminals of a battery
of 40 cells of Grove were brought within one-eighth of an inch of
each other, and the spark from a Leyden jar was sent across this
space. This spark bridged with carbon particles the gap which
had previously existed in the circuit, and the brilliant electric
light due to the passage of the battery current was immediately
displayed.
Influence of Magnetic Force on the Electric Discharge. 239
2. The magnified image of the coal-points of an electric lamp was
projected upon a -^'hite screen, and the distance to which they could
be drawn apart without interrupting the current was noted. A
button of pure silver was then introduced in place of the positive
carbon, a luminous discharge four or five times the length of the
former being thus obtained. The silver was first observed to glow,
and afterwards to pass into a state of violent ebullition. ^ narrow
dark space was observed to surround one of the poles, corresponding
probably with the dark space observed in the discharge of Ruhmkorflf's
coil through rarefied media*.
3. The action of a magnet upon the splendid stream of green light
obtained in the foregoing experiment was exhibited. A small horse-
shoe magnet of Logemann was caused to approach the light, which
was bent hither and thither according as the poles of the magnet
changed their position : the discharge in some cases formed a mag-
nificent green bow, which on the further approach of the magnet
was torn asunder, and the passage of the current thereby interrupted.
It was Davy who first showed the action of a magnet upon the
voltaic arc. The transport of matter by the current was further
illustrated by a series of deposits on glass obtained by Mr. Gassiot
from the continued discharge of an induction coil.
4. A discharge from Ruhmkorff's coil was sent through an at-
tenuated medium ; and the glow which surrounded the negative
electrode was referred to. One of the most remarkable eifects
hitherto observed was that of a magnet upon this negative light.
Pliicker had shown that it arranges itself under the influence of the
magnet exactly in the direction of the magnetic curves. Iron filings
strewn in sjiace, and withdrawn from the action of gravity, would
arrange themselves around a magnet exactly in the manner of the
negative light.
An electric lamp was placed upon its back ; a horseshoe magnet
was placed horizontally over its lens, and on the magnet a plate of
glass : a mirror inclined at an angle of 45° received the beam from
the lamp, and projected it upon the screen. Iron filings were
scattered on the glass, and the magnetic curves thus illuminated
were magnified, and brought to clear definition ui^on the screen. The
negative light above referred to arranges itself, according to Pliicker,
in a similar manner.
5. The rotation of an electric current round the pole of a magnet,
discovered by Mr. Faraday in the Royal Institution, nearly forty
years ago, was next shown ; and the rotation of a luminous current
from an induction coil in an exhausted receiver, by the same magnet,
was also exhibited, and both shown to obey the same laws. This
beautiful experiment was devised by De la Rive.
6. Into a circuit of 20 cells a large coil of copper wire was intro-
duced ; and when the current was interrupted, a bright spark, due to
the passage of the extra current, was obtained. The brightness and
* Mr. Faraday noticed this dai-k stripe while the speaker was making
his preparatory experiments.
240 Royal Institution : —
loudness of the spark were augmented when a core <5f soft iron was
placed within tlie coil. The disruption of the current took place
between the poles of an electro-magnet ; and when the latter
was excited, an extraordinary augmentation of the loudness of the
spark was noticed. This effect was first obtained by Page, and
was for a time thought to denote a new property of the electric
current.
But Rijke had shown, in a paper the interest of which is by no
means lessened by the modesty with which it is written, that the
effect observed by Page is due to the sudden extinction of the
primary spark by the magnet; which suddenness concentrates the
entire force of the extra current into a moment of time. Speaking
figuratively, it was the concentration of what, under ordinary cir-
cumstances, is a mere push, into a sudden kick of projectile
energ}-.
7. The contact-breaker of an induction coil was removed, and a
current from five cells was sent through the primary wire. The
terminals of the secondary wire being brought ver}- close to each
other, when the primary was broken by the hand, a minute spark
passed between the terminals of the secondary. When the dis-
ruption of the primary was effected between the poles of an excited
electro-magnet, the small spark was greatly augmented in brilliancy.
The terminals were next drawn nearly an inch apart. When the
primary was 'broken between the excited magnetic poles, the spark
from the secondary jumped across this interval, whereas it was in-
competent to cross one-fourth of the space when the magnet was
not excited. This result was also obtained by Piijke, who rightly
showed that in this case also the augmented energy of the secondary
current was due to the augmented speed of extinction of the primary
spark between the excited poles, 'lliis experiment illustrated in a
most forcible manner the important influence which the mode
of breaking contact may have upon the efficacy of an induction
coil.
The splendid effects obtained from the discharge of Ruhmkorff's
coil through exhausted tubes were next referred to. The presence
of the coil had complicated the theoretic views of philosophers with
regard to the origin of those effects ; the intermittent action of the
contact-breaker, the priman* and secondary currents, and their mu-
tual reactions, producing tertiary and other currents of a higher
order, had been more or less invoked by theorists to account for the
effects observed. Mr. Gassiot was the first to urge, with a water
battery of 3500 cells, a voltaic spark across a space of air, before
bringing the electrodes into contact ; with the self-same batterj- he
had obtained discharges through exhausted tubes, which exhibited
all the phsenomena hitherto observed with the induction coil. He
thus swept away a host of unnecessary complications which had
entered into the speculations of theorists upon this subject.
S. On the present occasion, through the kindness of Mr. Gassiot,
the speaker was enabled to illustrate the subject by means of a
battery of 400 of Grove's cells. The tension at the ends of the
Influence of Magnetic Force on the Electric Discharge. 241
battery was first shown by an ordinary gold-leaf electroscope ; one
end of the battery being insulated, a wire from the other end was
connected with the electroscope ; the leaves diverged ; on now con-
necting the other end of the battery with the earth, the tension of
the end connected with the electrometer rose, according to a well-
known law, and the divergence was greatly augmented.
9. A large receiver (selected from Mr. Gassiot's fine collection),
in which a vacuum had been obtained by filling it with carbonic acid
gas, exhausting it, and permitting the residue to be absorbed by
caustic potash, was placed cquatorially between the poles of the
large electro -magnet. The jar was about six inches wide, and the
distance between its electrodes was ten inches. The negative elec-
trode consisted of a copper dish, four inches in diameter ; the positive
one was a brass wire.
On the 16th of this month an accident occurred to this jar. Mr.
Faraday, Mr. Gassiot, and the speaker had been observing the dis-
charge of the nitric acid battery through it. Stratified discharges
passed when the ends of the battery were connected with the elec-
trodes of the receiver ; and on one occasion the discharge exhibited
an extraordinary effulgence ; the positive wire emitted light of daz-
zling brightness, and finally gave evidence of fusion. On inter-
rupting the circuit, the positive wire was found to be shortened about
half an inch, its metal having been scattered by the discharge over
the interior surface of the tube.
10. The receiver in this condition was placed before the audience
in the position mentioned above. When the ends of the 400-cell
battery were connected with the wires of the receiver, no discharge
2)assed ; but on touching momentarily with the finger any portion of
the wire between the positive electrode of the receiver and the po-
sitive pole of the battery, a brilliant discharge instantly passed, and
continued as long as the connexion with the battery was maintained.
This experiment was several times repeated : the connexion with
the ends of the battery was not sufficient to produce the discharge ;
but in all cases the touching of the positive wire caused the discharge
to flash through the receiver.
Previous to the fusion of the wire above referred to, this discharge
usually exhibited fine stratification : its general character now was
that of a steady glow, through which, however, intermittent lu-
minous gushes took ])lace, each of which presented the stratified
ap])earance.
11. On exciting the magnet between whose poles the receiver was
placed, the steady glow curved up or down according to the polarity
of the magnet, and resolved itself into a series of effulgent transverse
bars of liglit. These appeared to travel from the positive wire along
the surface of the jar. The deflected luminous current was finally
extinguished by the action of the magnet.
12. When the circuit of the magnet was made and immediately
interrupted, the appearance of the discharge was extremely singular.
At first the strata rushed from the positive electrode along the upper
242 Roj/al Institution.
sui'face of the jar, then stopped, and appeared to return upon their
former track, and pass successively with a deUberate motion into
the positive electrode. They were perfectly detached from each
other; and their successive engulfments at the positive electrode
were so slow as to he capable of being counted aloud with the grea est
ease. This deliberate retreat of the strata towards the positive pole
was due, no doubt, to the gradual subsidence of the power of the
magnet. Artificial means might probably be devised to render the
recession of the discharge still slower. The rise of power in the
magnet was also beautifully indicated by the deportment of the
current.
After the current had been once quenched, as long as the magnet
remained excited, no discharge passed ; but on breaking the magnet
circuit, the luminous glow reappeared. Not only, then, is there an
action of the magnet upon the particles transported by an electric
current, but the above experiment indicates that there is an action
of the magnet upon the electrodes themselves, which actually prevents
the escape of their particles. The influence of the magnet upon
the electrode would thus appear to be ijrior to the passage of the
current.
13. The discharge of the battery was finally sent through a tube
whose platinum wires were terminated by two small balls of carbon :
a glow was first produced ; but on heating a portion of the tube
containing a stick of caustic potash, the jjositive ball sent out a
luminous protrusion, which subsequently detached itself from the
ball, — the tube becoming instantly afterwards filled with the most
brilliant strata. There can be no doubt that th^ superior eflfulgence
of the bands obtained with this tube is due to the character of its
electrodes : tJie bands are the transported matter of these electrodes.
May not this be the case with other electrodes ? There appears to be
no uniform flow in nature ; we cannot get either air or water through
an orifice in a uniform stream ; the friction against the orifice is
overcome by starts, and the jet issues in pulsations. Let a lighted
candle be quickly passed through the air ; the flame will break itself
into a beaded line in virtue of a similar intermittent action, and it
may be made to sing, so regular are the pulses produced by its pas-
sage. Analogy might lead us to suppose that the electricity over-
comes the resistance at the surface of its electrode in a similar man-
ner, escaping from it in tremors, — the matter which it carries along
with it being broken up into strata, as a liquid vein is broken into
drops*.
* Mr. Gassiot has shown that a single discharf/e of the Leyilen jai- j)ro-
duces the stiatification. May not every such discharge correspond to a
single draw of a violin bow across a string ?
[ 243 J
XXXI. Intelliyence and Miscellaneous Articles.
ON THE COURELATION OP PHYSICAL, CHEMICAL, AND VITAL
FOIICE.
To the Editors of the Philosophical Magazine.
Gentlemen,
TN reference to the very interesting paper of Professor Le Conte's,
-■- published in the February Number of the Philosophical Magazine
(on the Correlation of Physical, Chemical, and \'ital Force), may I
take tlie liberty of calling your attention to the fact that a view in
many respects similar to his has been argued in a paper " On the
Theory of Inflammation," contributed by me to the British and
Foreign Medico-Chinirgical Review for July 1858 ?
Two or three sentences from that paper will suiBciently exhibit
the points of agreement. After a reference to the partial decomposition
in the egg and the seed, which is a condition of their development,
and to other instances, these words follow : — " Such facts as these
justify us in placing decomposition in organic tissues among the
circumstances which give rise to the organizing process." — P. 215.
At p. 222 is the following sentence : — " As a formative or vital pro-
cess, dependent on a decomposing or chemical one, it [inflammation]
corresponds to the clearest conception of nutrition that we can gather
from the pha?nomena of life in all its forms."
It is a great satisfaction to me to see views to which I had been
led, so much more ably and fully exhibited by an independent writer.
I am, Gentlemen,
Your obedient Servant,
James Hinton.
London, Fclnuarv 18G0.
ON THE COXDUCTIBILITY OF CERTAIN ALLOYS FOR HEAT AND
ELECTRICITY. BY G. WIEDEMANN.
In an experimental investigation, Wiedemann and Franz* found
that the thermal and electrical conductibility of metals was nearly
identical. Their researches also showed that in brass (which con-
tains 1 part of zinc to 2 of copper) the thermal conductibility differs
but very little from that of the worse conducting metal, zinc, although
the latter is present in smallest quantity. In other alloys, as those
of tin and lead, an analogous relation prevails in reference to the
electric conductibility. Messrs. Calvert and Johnson have lately
investigated the thermal conductibility of several alloys, and have
arrived at results which differ materially from those of Wiedemann
and Franz, and which render doubtful the analogy Avhich had been
• Phil. :Mag. [4] vol. vii. p. 33 ; vol. x. p. 393.
244 Intelligence and Miscellaneous Articles.
established between the thermal and electrical conductibllity. Wiede-
mann has accordingly determined the conductibility for heat and
electricity of several alloys. He used tlie same method as in the
previous researches, and the following Table contains the results at
which he has arrived. The standard adopted is silver, the conduc-
tibility of which, both for heat and electricity, is taken at 100.
8
Copper-zinc ^ denotes an alloy containing 8 parts of copper to 1 of
zinc.
Conductibilitv for
Heat.' Electricity.
Copper 73-6 79-3
8
Copper-Zinc - 27"3 25"5
6-5
Copper-Zinc ^L± 29-9
30-9
Copper-Zinc^ 31-1 29*2
Brass — 2j-8 25-4
Zinc 281 27-3
Tin 15-2 17-0
Tin-Bismuth 1 10" 1 90
Tin-Bismuth i 5-6 4-4
1
Tin-Bismuth | 2-3 20
Rose's Metal 4-0 3-2
From these results Wiedemann concludes —
1. That the agreement, which had been previously found to exist,
between the thermal and electrical conductibility of metals obtains
also for alloys.
2, That the conductibilities of alloys of zinc and copper, for
heat as well as for electricity, differ but little, even with a consider-
able excess of copper, from the conductibility of the worse conducting
metal, zinc. The alloys of zinc and bismuth, on the contrary, have
nearly the mean conductibility calculated from their atomic com-
position.—Poggendorff's Annalen, Nov. 1859.
THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
APRIL 1860.
XXXII. On the Effect of the Motion of a Body upon the Velocity
with which it is traversed by Light. By M. H. Fizeau*.
MANY theories have been proposed with a view of accounting
for the phgenomenon of the aberration of light according
to the undulatory theory. In the first instance Fresnel, and
more recently Doppler^ Stokes, Challis, and several others have
published important researches on this subject; though none of
the theories hitherto proposed appear to have received the com-
plete approval of physicists. Of the several hypotheses which
have been necessitated by the absence of any definite idea of the
properties of luminiferous tether, and of its relations to ponder-
able matter, not one can be considered as established; they merely
possess different degrees of probability.
On the whole these hypotheses may be reduced to the follow-
ing three, having reference to the state in which the aether ought
to be considered as existing in the interior of a transparent body.
Either, first, the tether adheres or is fixed to the molecules of the
body, and consequently shares all the motions of the body ; or
secondly, the tether is free and independent, and consequently
is not carried with the body in its movements ; or, thirdly, only
a portion of the tether is free, the rest being fixed to the mole-
cules of the body and, alone, sharing its movements.
The last hypothesis was proposed by Fresnel, in order at once
* Translated from the Annales de Chimie et de Physique for December
1859. The original memoir was presented to the Parisian Academy of
Sciences, Sept. 29, 1851 ; and a translation of the brief abstwwtTTTTtrlished
in the Comptes Rendus was given in the Phil. Mag. for December 1851,
p. 5(58.
PMl. Mag, S. 4. Vol. 19. No. 127. April 1860. S
246 M. H. Fizeau on the Effect of the Motion of a Body
to satisfy the conditions of the aberration of light and of a cele-
brated experiment of Arago^s, which proved that the motion of
the earth does not aflfect the value of the refraction suffered by
the light of a star on passing through a prism. Although these
two pha?nomena may be explained with admirable precision by
means of this h\^othesis, still it is far from being considered at
present as an established truth, and the relations between Eether
and matter arc still considered, by most, as unknown. The
mechanical conception of Fresnel has been regarded by some as
too extraordinaiy to be admitted without direct proofs ; others
consider that the observed phsenomena may also be satisfied by
one of the other hypotheses ; and others, again, hold that certain
consequences of the hypothesis in question are at variance with
experiment.
The following considerations led me to attempt an experiment
the result of which promised, I thought, to throw light on the
question.
It will be observed that, according to the first hypothesis, the
velocity with which light traverses a body must vary with the
motion of that body. If the motions of the body and the ray
are like-directed, the velocity of light ought to be increased by
the whole velocity of the body.
If the ffither be perfectly free, the velocity of light ought not
to be altered by the motion of the body.
Lastly, if the body when moving only carries with it a portion
of the sether, then the velocity of light ought to be increased by
a fractional part of the velocity of the body and not by the whole
velocity, as in the first case. This consequence is not as evident
as the two preceding ones, though Fresnel has shown that it is
supported by mechanical considerations of a very probable nature.
The question then resolves itself to that of determining with
accuracy the effect of the motion of a body upon the velocity
with which light traverses it.
It is true that the velocity with which light is propagated is
so immensely superior to any we are able to impart to a body,
that any change in the first velocity must in general be inappre-
ciable. Nevertheless, by combining the most favourable cir-
cumstances, it appeared to be possible to submit to a decisive
test at least two media, air and water, to which, on account
of the mobility of their particles, a great velocity may be im-
parted.
AVe owe to Arago a method of observation, founded on the
phfenomena of interference, which is well suited to render evident
the smallest variation in the index of refraction of a body, and
hence also the least change in the velocity with which the body
is traversed by Hght ; for, as is well known, this velocity is in-»
upon the Velocity ivith which it is travo'sed by Light: %\T
versely proportional to the refracting index. Arago and Fresncl
have hoth shown the extraordinary sensitiveness of this method
by several very delicate observations, such as that on the difference
of refraction between dry and moist air.
A method of observation founded upon this principle appeared
to rae to be the only one capable of rendering evident any change
of velocity due to motion. It consists in obtaining interference
bands by means of two rays of light after their passage through
two parallel tubes, through which air or water can be made to
flow with great velocity in opposite directions. The especial
object before me necessitated several new arrangements, which I
proceed to indicate.
With respect to the intensity of light, formidable difficulties
had necessarily to be encountered. The tubes, which were of
glass and 5*3 millims, in diameter, had to be traversed by light
along their centres, and not near their sides ; the two slits, there-
fore, had to be placed much fui'ther apart than is ordinarily the
case, on which account the light would, in the absence of a spe-
cial contrivance, have been very feeble at the point where the
interference bands are produced.
This inconvenience was made to disappear by placing a con-
vergent lens behind the two slits; the bands were then observed
at the point of concourse of the two rays, where the intensity of
light was very considerable.
■ The length of the tubes being tolerably great, 1'487 metre,
it was to be feared that some diflerence of temperature or pres-
sure between the two tubes might give rise to a considerable
displacement of the bands, and thus completely mask the dis-
placement due to motion.
This difficulty was avoided by causing the two rays to return
towards the tubes by means of a telescope carrying a mirror at
its focus. In this manner each ray is obliged to traverse the two
tubes successively, so that the two rays having travelled over
exactly the same path, but in opposite directions, any effect due
to difference of pressure or temperature must necessarily be eli-
minated by compensation. By moans of various tests I assured
myself that this compensation was complete, and that what-
ever change in the temperature or density of the medium
might be produced in a single tube, the bands would preserve
exactly the same position. According to this arrangement, the
bands had to be observed at the point of departure itself of the
rays : solar light was admitted laterally, and was directed towards
the tubes by means of reflexion from a transparent mirror; after
their double journey through the tubes, the rays returned and
traversed the mirror before reaching the place of interference,
where the bands were observed by means of a graduated eye-piece.
S2
248 M. H. Fizeau on the Effect of the Motion of a Body
The double journey performed by the rays had also the
advantage of increasing the probable eftect of motion j for this
effect must be the same as if the tubes liad double the length
and were only traversed once.
Tliis arrangement also permitted the employment of a very
simple method for rendering the bands broader than they would
otherwise have been in consequence of the great distance (9
millims.) between the slits. This method consisted in placing a
very thick plate of glass before one of the slits, and inclining the
same in such a manner that, by the effect of refraction, the two
slits had the appearance of being very close to each other : in
this manner the Ijands become as broad as they would be if the
two slits were, in reality, as near each other as they appear to be ;
and instead of the intensity of light being sensibly diminished
by this expedient, it may, in fact, be greatly augmented by giving
greater breadth to the source of light. By causing the inclina-
tion of the glass to vary, the breadth of the bands may be varied
at pleasure, and thus the magnitude most convenient for pre-
cisely observing their displacement may be readily given to them.
I proceed to describe the disposition of the tubes, and the
apparatus destined to put the water in motion.
The two tubes, placed side by side, were closed at each ex-
tremity by a single glass plate, tixed with gum-lac in a position
exactly perpendicular to their common direction. Near each
extremity was a branch tube, forming a rounded elbow, which
established a communication with a broader tube reaching to the
bottom of a flask ; there were thus four flasks communicating
with the four extremities of the tubes.
Into one flask, which we will suppose to be full of water, com-
pressed air, borrowed from a reservoir furnished with an air-
pump, was introduced through a communicating tube. Under
the influence of this pressure the water rose from the flask into
the tube, which it then traversed in order to enter the flask at
the opposite end. The latter could also receive compressed air,
and then the liquid returned into the first flask after traversing
the tube in an opposite direction. In this manner a current of
water was obtained whose velocity exceeded 7 metres per second.
A similar current, but in an opposite direction, was produced at
the same time in the other tube.
Within the observei-'s reach were two cocks fixed to the re-
servoir of air ; on opening either, cuirents, opposite in direction,
were established in both tubes ; on opening the other cock the
currents in each tube were simultaneously reversed.
The capacity of the reservoir, containing air at a pressure of
about two atmospheres, amounted to 15 litres (half a cubic foot),
that of each flask to about 2 litres ; the latter were divided into
upon the Velocity with which it is traversed by Light. 249
equal volumes, and the velocity of the water was deduced from
the section of the tubes, and from the time of efflux of half a litre.
The apparatus above described was only employed for the ex-
periments with water iu motion : with some modifications it
might also be used for air; but my experiments on moving air
had been previously made with a slightly difi'erent apparatus, of
which more hereafter, and the results had been found quite con-
clusive, I had already proved that the motion of air produces no
appreciable displacement of the bands. But I shall return to this
result and give further details.
For water there is an evident displacement. The bands are
displaced towards the riyht when the icater recedes from the ob-
server in the tube at his right, and approaches him in the tube on
his left.
The displacement of the bands is towards the left when the direc-
tion of the current in each tube is opposite to that just defined.
During the motion of the water the bands remain well defined,
and move parallel to themselves, without the least disorder,
through a space apparently proportional to the velocity of the
water. With a velocity of 2 metres per second even, the dis-
placement is perceptible ; for velocities between 4 and 7 metres
it is perfectly measureable.
In one experiment, where a band occupied five divisions of the
micrometer, the displacement amounted to 1 "2 divisions towards
the right and 1*2 divisions towards the left, the velocity of the
water being 7'059 metres per second. The sum of the two dis-
placements, therefore, was equal to 2'4 divisions, or nearly half
the breadth of a band.
In anticipation of a probable objection, I ought to state that
the system of the two tubes and four flasks, in which the motion
of the water took place, was quite isolated from the other parts
of the apparatus : this precaution was taken in order to prevent
the pressure and shock of the water from producing any acci-
dental flexion in parts of the apparatus whose motion might in-
fluence the position of the bands. I assured myself, however,
that no such influence was exerted, by intentionally imparting
motions to the system of the two tubes.
After establishing the existence of the phpenomenon of dis-
placement, I endeavoured to estimate its magnitude with all
possible exactitude. To avoid all possible sources of error, I
varied the magnification of the bands, the velocity of the water,
and even the nature of the divisions of the micrometer, so as to
be unable to predict the magnitude of the displacements before
measuring them. For in measuring small quantities, where our
own power of estimating has to play a great part, the influence
of any preconception is always to be feared ; I think, however,
250 M. H. Fizcau on the Effect of the Motion of a Body
that the result 1 have obtained is altogether free from this cause
of error.
For the most part the observations were made with a velocity
of 7'059 metres per second ; in a certain number the velocity
was 5"515 metres, and in others 3'7 metres. The magnitudes
observed have been all reduced to the maximum velocity 7*059
metres, and referred to the breadth of a band as unity.
Displacements of the Differences between the
bands for a mean velocity obsen'ed displacements
of water equal to 7"059 and their mean value,
metres per second.
0-200 -0-030
0-220 -0-010
0-240 +0-010
0-167 -0-0G3
0-171 -0-059
0-225 -0-005
0-247 -f 0-017
0-225 -0-005
0-214 -0016
0-230 0-000
0-224 -0006
0-247 +0-017
0-224 -0-006
0-307 +0-077
0-307 +0-077
0-256 +0-026
0-240 +0-010
0-240 +0-010
0-189 -0041
Sum . 4-373
' Mean . 0-23016
By doubling the mean value we have 0-46, nearly half the
breadth of a band, which represents the magnitude of the dis-
j)lacement produced by reversing the direction of the current in
each tube.
To show the deviations on each side, the differences between
the several observed displacements and the mean value of all
have been inserted in the Table. It will be seen that, in general,
they represent a very small fraction of the breadth of a band ;
the greatest deviation does not exceed one-thirteenth of the
breadth of a band.
These differences are due to a difficulty which could not be
overcome ; the displacehient remained at its maximum but for a
very short period, so that the observations had to be made very
upon the Velocity ivith which it is traversed by Light. 251
rapidly. Had it been possible to maintain the velocity of the
current of water constant for a greater length of time, the mea-
surements would have been more precise; but this did not
appear to be possible without considerably altering the appa-
ratusj and such alterations would have retarded the prosecution
of my research until the season was no longer favourable for
experiments requiring solar light.
I proceed to compare the observed displacement with those
which would result from the first and third hypotheses before
alluded to. As to the second hypothesis, it may be at once
rejected ; for the very existence of displacements produced by the
motion of water is incompatible with the supposition of an sethev
perfectly free and independent of the motion of bodies.
In order to calculate the displacement of the bands under the
supposition that the sether is united to the molecules of bodies
in such a manner as to partake of their movements, let
V be the velocity of light in a vacuum,
v' the velocity of light in water when at rest,
u the velocity of the water supposed to be moving in a direc-
tion parallel to that of the light. It follows that
y + u IS the velocity of light when the ray and the water move
in the same direction, and
v' — u when they move in opposite directions.
If A be the required retardation and E the length of the
column of water traversed by each ray, we have, according to the
principles proved in the theory of the interference of light,
\v—u v' + u/
or
A = 2E-
t/2-j
Since u is only the thirty-three millionth ])art of v, this expres-
sion may, without appreciable error, be reduced to
A=2E!i '
V
,i-Z'
If )n= -J be the index of refraction of water, we have the ap-
proximate formula
A = 2E-m2.
V
Since each ray traverses the tubes twice, the length E is double
the real Icngtli of the tubes. Calling the latter L = 1 '4875 metre,
253 ^I. H. Fizeau on the Effect of the Motion of a Body
the preceding formula becomes
V
and tlie numerical calculation being performed, we find
A = 0-000241 8 millim.
Such is the difference of path which, under the present hypo-
thesis, ought to exist between the two rays.
Strictly speaking, this number has reference to a vacuum, and
ought to be divided by the index of refraction for air; but this
index differs so little from unity, that, for the sake of simplicity,
the correction, which would not alter the last figure by a unit,
may be neglected.
The above quantity being divided by the length of an undula-
tion, will give the displacement of the bands in terms of the
breadth of one of them. In fact, for a difference of path amount-
ing to 1, 2, . . . 7?j undulations, the system of bands suffer a dis-
placement equal to the breadth of 1, 2, . . . m bands.
For the ray E the length of an undulation is X = 0'000526,
and the rays about it appear to preserve the greatest intensity
after the light has traversed a rather considerable thickness of
water. Selecting this ray, then, we find for the displacement
the value
^=0-4597.
Had, therefore, the aether ])articipatcd fully in the motion of
the water, in accordance with the hypothesis under consideration,
a displacement of 0"46 of a band Avould have been observed in
the foregoing experiments. But the mean of our observations
gave only 0'23 ; and on examining the greatest particular values,
it will be found that none approached the number 0"46. I may
even remark that the latter number ought to be still greater, in
consequence of a small error committed in the determination of
the velocity of the water; an error whose tendency is known,
although, as will soon be seen, it was impossible to correct it
perfectly.
I conclude, then, that this hypothesis does not agree with ex-
periment. We shall next see that, on the contrary, the third, or
FresneFs hypothesis, leads to a value of the displacement which
differs very little from the result of observation.
We know that the ordinary pha3nomena of refraction are due
to the fact that light is propagated with less velocity in the in-
terior of a body than in a vacuum. Fresnel supposes that this
change of velocity occurs because the density of the asther within
a body is greater than that in a vacuum. Now for two media
upon the Velocity with which it is travo'sed hy Light. 253
whose elasticity is the same, and which differ only in their den-
sities, the squares of the velocities of propagation are inversely
proportional to these densities ; that is,
D and D' being the densities of the sether in a vacuum and in
the body, and v, v^ the corresponding velocities. From the above
we easily deduce the relations
,,2 -,2 »/2
XJ —U ^,^, SJ XJ — U ^j2 >
the latter of which gives the excess of density of the interior
sether.
It is assumed that \vhen the body is put in motion, only a part
of the interior sether is carried along with it, and that this part
is that which causes the excess in the density of the interior
over that of the surrounding sether ; so that the density of this
moveable part is D'— D. The other part which remains at rest
during the body's motion has the density D.
The question now arises. With what velocity will the waves be
propagated in a medium thus constituted of an immoveable and
a moveable part, when for the sake of simplicity we suppose the
body to be moving in the direction of the propagation of the
waves ?
Fresnel considers that the velocity with which the waves arc
propagated then becomes increased by the velocity of the centre
of gravity of the stationary and moving portions of sether. Now
u being the velocity of the body,
D'-D
u
D'
will be the velocity of the centre of gravity of the system in
question, and according to the last formula this expression is
equal to
v^ — t/'^
Such, then, is the quantity by which the velocity of light will be
augmented ; and since z;' is the velocity when the body is at rest,
II and v ; — u
V
will be the respective velocities when the body moves with and
against the light.
By means of these expressions the corresponding displacement
of the bands in our experiment may be calculated in exactly the
^54 M.U. Fizeaii on the Effect of the Motion of a Body
same tnamu'r as before. For the difference of path wc liavc the
vahie
which by reduction and transformation becomes
''''-»\-ir)
Taking into consideration the smalhiess of u witli respect to
^'( ~7 = o yr^r\rM^r^(^ )} ^"^^ ^^^^ circumstance that the coefficient of
\r' ooOuOUOU /
u'^ differs little from unity^ the term in u^ may, without appre-
ciable error, be neglected, and the above expression considerably
simplified. In fact, if m be the index of refraction, and L = iE
the length of each tube, we have approximately
A = 4L-(m'^-l),
V
whence by numerical calculation we deduce
A = 0-00010634 millim.
On dividing this difference of path by the length \ of an undu-
lation, the magnitude of the displacement becomes
^ = 0-2022,
A,
the observed value being 0*23.
These values are almost identical ; and what is more, the dif-
ference between observation and calculation may be accounted
for with great probability by the presence of the before-mentioned
error in estimating the velocity of the water. I proceed to show
that the tendency of this error may be assigned, and that ana-
logy permits us to assume that its effect must be very small.
The velocity of the water in each tube was calculated by divi-
ding the volume of water which issued per second from one of
the flasks by the sectional area of the tube. But by this method
it is only the mean velocity of the water which is determined ; in
other words, that which would exist provided the several threads
of liquid at the centre and near the sides of the tube moved with
equal rapidity. It is evident, however, that this cannot be the
case ; for the resistance opposed by the sides of the tube, acting
in a more immediate manner on the neighbouring threads of
liquid, tends to diminish their velocity more than it does that of
the threads nearer the centre of the tube. The velocity of the
upon the Velocittj tbith which it is traversed hy Light. 255
water in the centre of the tubes, therefore, must be greater than
that of the water near the sides, and consequently also greater
than the mean of both velocities.
Now the slits placed before each tube to admit the rays whose
interference was observed, were situated in the middle of the cir-
cular ends of the tubes ; so that the rays necessarily traversed the
central zones, where the velocity of the water exceeded the mean
velocity*.
The law followed by these variations of velocity in the motion
of water through tubes not having been determined, it was not
possible to introduce the necessary corrections. Nevertheless
analogy indicates that the error resulting therefrom cannot be
considerable. In fact, this law has been determined in the case
of water moving through open canals, where the same cause
produces a similar effect ; the velocity in the middle of the canal
and near the surface of the water is there also greater than the
mean velocity. It has been found that, for values of the mean
velocity included between 1 and 5 metres per second, the maxi-
mum velocity is obtained by multiplying this mean velocity by a
certain coefficient which varies from 123 to I'll. Analogy
therefore permits us to assume that in our case the con-ection
to be introduced would be of the same order of magnitude.
Now on multiplying u by I'l, 1-15, and 1-2, and calculating
the corresponding values of the displacement of the bands, we
find in place of 0-20 the values 0-22, 0-23, 0-24 respectively;
wlience it will be seen that in all })robability the correction woiild
tend to cause still greater agreement between the observed and
the calculated results. We may presume, then, that the small
difference which exists between the two values depends upon a
small error in estimating the real velocity of the water; which
error cannot be rectified in a satisfactory manner, in consequence
of the absence of sufficiently accurate data.
Thus the displacement of the bands caused by the motion of
water, as well as the magnitude of this displacement, may be
explained in a satisfactory manner by means of the theory of
Fresnel.
It was before observed that the motion of air causes no per-
ceptible displacement of the bands produced by the interference
of two rays which have traversed the moving air in opposite di-
rections. This fact was established by means of an apparatus
which I will briefly describe.
A pair of bellows, loaded with weights and worked by a lever,
impelled air forcibly through two parallel copper tubes whose
extremities were closed by glass plates. The diameter of each
* Each slit was a rectangle '6 milliuis. by 1"5, aUil its surface was equal
to one-fifth that of the tube.
256 M. H. Fizeau on the Effect of the Motion of a Body
tube was 1 centimetre, and its effective length 1"495 metre;
the direction of the motion in one tube was opposite to that in
the other^ and the pressure under which this motion took place
was measured by a manometer placed at the entrance of the
tubes ; it could be raised to 3 centimetres of mercury.
The velocity of the air was deduced from the pressure and
from the dimensions of the tubes, according to the known laws
of the efflux of gases. The value thus found was checked by
means of the known volume of the bellows, and the number of
strokes necessary to produce a pi'actically constant pressure at the
entrance of the tubes. A velocity of 25 metres per second could
easily be imparted to the air ; occasionally greater velocities were
reached, but their values remained uncertain.
In no experiment could a perceptible displacement of the
bands be produced : they always occupied the same positions,
no matter whether the air remained at rest, or moved with a
velocity equal or even superior to 25 metres per second.
AVhen this experiment was made, the possibility of doubling,
by means of a reflecting telescope, the value of the displacement,
and at the same time of completely compensating any effects due
to accidental diflferences of temperature or pressure in the two
tubes, had not suggested itself; but I employed a sure method
of distinguishing between the effects due to motion, and those
resulting from accidental circumstances.
This method consisted in making two successive observations,
by causing the rays to traverse the apparatus in opposite direc-
tions. For this purpose the source of light was placed at the
point where the central band had previously been, when the new
bands formed themselves where the source of light had previously
been placed.
The direction of the motion of the air in the tubes remaining
the same in both cases, it is easy to see that the accidental effects
would in both observations give rise to a displacement towards
the same tube, whilst the displacement due solely to motion
would first be on the side of one tube and then on the side of
the other. In this manner a displacement due to motion would
have been detected with certainty, even if it had been accom-
panied by an accidental displacement due, for instance, to some
defect of syumietry in the diameters or orifices of the tubes,
whence would result an unequal resistance to the passage of air,
and consequently a difference of density.
But the symmetry given to the apparatus was so perfect that
no sensible difference of density existed in the two tubes during
the motion of the air. The double observation was consequently
unnecessary ; nevertheless it was made for the sake of greater
security, and in order to be sure that the sought displacement
upon the Velocity with which it is traversed ly Light. 257
was not accidentally compensated by a difference of density,
which, though small, might be sufficient totally to mask such
displacement.
Notwithstanding these precautions, however, no displacement
of the bands occurred in consequence of the motion of the air;
and according to an estimate I have made, a displacement equal
to one-tenth of the breadth of a band would have been detected
had it occurred.
The calcujations with respect to this experiment are as fol-
lows. Under the hypothesis that the air, when moving, carries
with it all the sether, we have
A = 2L-m2= 00002-41 3 millim.,
V
rr? being equal to 1-000567 at the temperature 10° C.
This experiment having been made in air, the maximum illu-
mination was due to the yellow rays ; and this maximum deter-
mined the breadth of the bands. Hence the value of \ corre-
sponding to the ray D being taken, we have
^=0-4103.
A,
Now so great a displacement could certainly not have escaped
observation, especially since it might have been doubled by re-
versing the current.
The following would be the results of the calculation accord-
ing to the hypothesis of Fresnel : —
A = 2L-(/«2_i) =0-0000001307,
V
^ = 00002325.
A.
Now a displacement equal to j^Vo^^ ^^ *^^ breadth of a band
could not be observed ; it might, in fact, be a hundred times
greater and still escape observation. Thus the ai)parcnt immo-
bility of the bands in the experiment made with moving air may
be explained by the tlieory of Fresnel, according to which the
displacement in question, although not absolutely zero, is so small
as to escape observation.
After having established this negative fact, and seeking, by
means of the several hypotheses respecting ?ethcr, to explain it
as well as the pha?nomenon of aberration and the experiment of
Arago, it appeared to me to be necessary to admit, with Fresnel,
that the motion of bodies changes the velocity with which light
traverses them, but that this change of velocity varies according
to the energy with which the traversed medium refracts light ; so
958 M. II. Fizeau on the Effect of the Motion of a Body
that the cliangc is great for highly refracting bodies, hut small
for feebly refracting ones such as air.
I was thus led to anticipate a sensible displacement of the
bands by means of the motion of water, since its index of refrac-
tion greatly exceeds that of air.
It is true that an experiment of Babinet's, mentioned in the
ninth volume of the Comptes Rendus, appeared to be in contra-
diction to the hypothesis of a change in the velocity of light in
accordance with the law of Fresnel. But on considering the
conditions of that experiment, I detected the existence of a cause
of compensation whose influence would render the effect due to
motion insensible. This cause proceeds from the reflexion which
the light suffers in the experiment in question. It may, in fact,
be demonstrated that if a certain difference of path exists be-
tween two rays, that difference becomes altered when these rays
suffer reflexion from a moving mirror. Now on calculating
separately the two effects (of reflexion) in the experiment of
Babinet, their magnitudes will be found to be equal and oppo-
site in sign.
This explanation rendered the hypothesis of a change of velo-
city still more probable, and induced me to undertake the expe-
rmient with water, as being the most suitable one for deciding
the question with certainty.
The success of this experiment must, I think, lead to the
adoption of the hypothesis of Eresnel, or at least to that of the
law discovered by him, which expresses the relation between the
change of velocity and the motion of the body ; for although the
fact of this law being found to be true constitutes a strong argu-
ment in favour of the hypothesis of which it is a mere conse-
quence, yet to many the conception of Fresnel will doubtless still
appear both extraordinary and, in some respects, improbable ;
and before it can be accepted as the expression of the real state
of things, additional proofs will be demanded from the physicist,
as well as a thorough examination of the subject from the ma-
thematician.
Shortly before the publication of the above interesting memoir
in the Annates de Chimie, M. Fizeau presented to the Academy
a second memoir, containing the results of his experiments on
the effect of the motion of a transparent solid body, such as glass,
upon the velocity with which it is traversed by light. The
Comptes Rendus of November 14th, 1859, contains a brief ex-
tract from this memoir ; and from it we gather the principal re-
sults of his experiments, and the principles upon which the same
were based.
The method of experiment which was employed in the fore-
upon the Velocity roifh which it is iratm^sed hy Light. 259
going researches on air and water being no longer applicable,
recourse was bad to tbc following property of light established
by the researches of Malus, Biot, and Brewster. AMien a ray of
polarized light traverses a plate of glass, inclined towards its
direction, the plane of polarization of the transmitted ray is in
general inclined towards that of the incident ray. Tbc magnitude
of the rotation of the plane of polarization which is thus caused
by the two refractions at the two surfaces of the plate of glass
depends, first, upon the angle of incidence ; secondly, upon the
azimuth of the primitive plane of polarization with reference to
the plane of incidence ; and thirdly, upon the index of refraction
of the glass forming the plate.
The angle of incidence and the azimuth of the primitive plane
of polarization remaining the same, the rotation of this plane
increases with the index of refraction of the glass plate. Now
since this index is inversely proportional to the velocity with
which waves of light are propagated through the glass, it follows
that the magnitude of the rotation of the plane of polarization
increases when the velocity with which light traverses the glass
plate diminishes. The determination of any change in this
velocity is, therefore, reduced to that of the corresponding change
in the rotation of the plane of polarization.
In the first place it was deemed necessary to determine the
change in the rotation which any given increase or decrease of
the index of refraction could produce. By direct and comparative
measurements of these indices and rotations, in the cases of flint
and ordinary glass, it was found that when the index was in-
creased by a small fraction, the rotation increased by a fraction
41 times greater than the first.
The question, next arises what change, according to the hypo-
thesis of Fresnel, ought to be produced in the velocity of light
when it traverses glass in a state of motion ? The answer is
based upon the following data.
The greatest velocity at our command is unquestionably that
of the earth in its orbit. At noon, during the ])eriod of the sol-
stices, for instance, the direction of this motion is horizontal and
from east to west j from this it follows that when a plate of glass
receives a ray of light coming from the west, it ought to be con-
sidered as really moving to meet the ray with the immense velo-
city of 31,000 metres per second. \^ hen, on the contrary, the
incident ray comes from the east, the glass plate nuist be con-
sidered as moving with this velocity in the same direction as that
of the propagation of the waves of light, by which latter it is in
reality overtaken.
Now, according to the theory of Fresnel, the difterence between
the velocities of the light in these two extreme cases would be
260 0« the Effect of the Motion of a Body on Light,
sufficient to produce a change in tlic rotation of the plane of
polarization equal to jjoo^^ P^^'^ ^^ ^^® magnitude of that
rotation.
In order to test this result by experiment, a series of glass
plates were interposed in the path of a polarized beam of parallel
rays of light. The primitive plane of polarization was determined
by a divided circle, and the rotation which this plane underwent
by the action of the plates was measured by means of a second
graduated circle fixed to a convenient analyser. The instrument
could, moreover, be fixed in any direction so as to study the in-
fluence of all terrestrial motions upon the phsenomena.
In order to make the two necessary observations conveniently
and rapidly, two mirrors were previously fixed on the east and on
the west of the instrument, and upon each, alternately, a beam
of solar light was thrown by means of a heliostat, and thence re-
flected towards the instrument.
The greatest difficulties were encountered in the annealing of
the glass plates of the series ; and as perfectly homogeneous
plates could not be obtained, it was necessary to employ various
compensating expedients, all which will be found described in
the memoir itself.
The conclusions to which IM. Fizeau was led by means of more
than 2000 observations are thus stated : — :
1. The rotation of the plane of polarization produced by a
series of inclined glass plates is always greater when the light
which traverses them comes from the west than when it comes
from the east ; the observation being made about noon.
2. This excess of rotation is decidedly at a maximum at or
about noon during the solstices. Before and after this hour it
is less, and at about 4 o'clock is scarcely perceptible.
3. The numerical values deduced from the numerous series of
observations present notable differences, the cause of which may
be guessed, though it cannot yet be determined with certitude.
4. The influence of the earth's annual motion, as determined
by calculation on the hypothesis of Fresnel, leads to values of
the above excess of rotation which agree tolerably well with the
majority of the values deduced from observation.
5. Theory, as well as experiment, therefore, lead us to con-
clude that the azimuth of the plane of polarization of a refracted
ray is really influenced by the motion of the refracting medium,
and that the motion of the earth in space exerts an influence of
this kind upon the rotation of the plane of polarization produced
by a series of inchued glass plates.
[ 261 ]
XXXIII. On a neiu Instrument for the Mechanical Trisectiun of
an Angle; and on the Multisection of an Angle. By Thomas
Tate, Esq,*
THE trisection of an angle is a subject of historical celebrity,
and, apart from its utility, must always be interesting to
the mathematician. Some years ago, Professor Christie invented
an instrument for the mechanical trisection of an angle, which
consists of four rods, kept at equal angles apart from each other
by means of linkwork. Although simple in principle, this in-
strument is somewhat complicated in construction, and therefore
necessarily, to some extent, inaccurate as regards its application.
This instrument contains four rods, ten links, ten axes, and two
sliding-pieces ; whereas the instrument which I have made con-
tains only two rods, four links, four axes, and two sliding-piecea.
Both instruments are mathematically correct in principle.
The instrument
which I have con-
structed is represent-
ed in the annexed
diagram. A B and
A C are two rods
turning on the axis
A; DE, DF, D H,
and D G are four
links, each equal in
length to AEor AF,
turning on a common
axis D, D E being
connected with A B
by an axis at E, and
D F with A C by an
axis at F, The pin
G, of the link D G,
slides in the slit a b
formed in the rod
A B in the line of
the axes A and E ;
and the pin H, of
the link l) II, slides
HI the slit ec formed in the rod AC in the line of the axes A
and F. The inner edges of the four hnks, 1) E, D F, D H, D G,
are in a line with the centres of their respective axes, as shown
in the diagram The rods A B and A C are connected by a half-
lap joint at A ; and similarly the four links are connected at D
by half-lap joints, so that the pieces all lie Hat upon the surface
* Coniniunicated by the Author.
Phil. Mag. S. 1. Vol. 19. No. Ul . April. 1860. T
262 On an Instrument for the Mechanical Triseciion of on Angle.
of the paper. The links D E, 1) V, D II, I) G lie bclo\v the rods
A B and A C at their resjiective points of coiniexion, so that the
plane of A B C always lies parallel to the plane of the paper.
The instrnment is used in the following manner.
Let K D L be the angle to be trisected. Produce K D to H,
and L D to G. Laying hold of the extremities B and C of the
rods AB and AC, move the links DH and DG until their inner
edges coincide with the lines forming the angle G D H ; draw
lines D E, D F along the inner edges of the links DE and DF ;
then these lines will trisect the given angle K D L, as required.
Demonstration. — In all positions of the instrumeiit, AEDF is
an equilateral parallelogram, and DGE, DHF are equal isosceles
triangles.
Because DG = DE, ZGED=ZDGE; and because DF is
parallel to EG, zLDF=zDGE; therefore zLDF=zGED;
but because DF is parallel to EG, ZEDF= Z GED ; therefore
ZLDF= zEDF.
In like manner it may be sho\\Ta that ZKDE= ZEDF;
therefore the lines DF and DE trisect the angle KDL.
I have made this instrument of lance-wood, with brass pivots.
The links are each 8 inches long, ^ of an inch in width, and
y^^ths of an inch in thickness. By means of this instrument,
any angle not much exceeding two right angles and not less than
nine degrees, may be at once trisected with great precision ; but
by an obvious mathematical artifice it may be used for the tri-
section of angles, however small or large they may be.
It is scarcely neces-
sary to observe, that
all general methods
for the multisection
of a given arc can only
be approximate. In
such cases there can
be no objection to the
use of approximate
methods of construc-
tion, provided that
theyaregiven assuch.
By the following me-
thod of construction,
a given arc may be
divided into any num-
ber of equal parts,
with an approach to
truth which is only
limited by the iuac-
On certain Laws of Chromatic Dispersion. 263
curacies necessarily involved in the drawing of lines through
points formed by the intersection of straight lines or circular
arcs.
Let it be required to divide the given arc A B D, whose
centre is C, into any number of equal parts. (In the example
here given, the arc is divided into seven equal parts.)
First approximation. — Bisect the given arc in G, and draw
the chord AG. Through A draw the diameter ACB, and divide
it into n equal parts in the points 1, 2, 3, &c. Bisect the chord
A G by the perpendicular F C 0 ; from A and B as centres, with
the diameter A B as radius, describe arcs cutting each other in
K ; and from the centre C, with C K as a radius, describe the
arc K 0, cutting F C 0 in 0. Through the point 2 draw 2 E
|)arallel to 0 F, meeting A G in E ; and through E and 0 draw
the straight line 0 E <?, meeting the arc in a ; then A a will be
approximately the nth. part of the arc A G B D, but which may
be determined with greater precision as follows.
Second approximation. — Take off the chord A a in the com-
passes, and apply it on the arc iV G D proceeding from a towards
D ; let ^ be the last point in the division ; apply this chord from
D to p, and join/* C. Bisect A 1 in m ; from the centre C, with
C m as a radius, describe an arc cutting Cpin e ; through e
draw e n parallel to C k, cutting the arc in the point n ; then D n
will be practically the nth part of the given arc A G B D, as
required.
When the number of parts into which the given arc is to be
divided is considerable, especially when the arc is equal to or
nearly equal to the whole circumference of the circle, the second
operation in the foregoing process becomes necessary in order to
attain a sufficient degree of accuracy.
The proposition contained in the first approximation is a
generalization of a well-known method, sometimes employed by
practical men, for the division of the whole circumference of the
circle into a given number of equal parts.
Hastings, March 6, 1860.
XXXIV. On certain Laws of Chromatic Dispersion.
By MuNGo roxTON, F.R.S.E.
[Coiitiiuied from p. 181.]
WITH a \'iew to an examination of the results arrived at in
the previous part of this paper, it will be found con-
venient to classify the observations. Fraunhofer has fortu-
nately given two sets of observations for water, and also for
fiint-glass No. 23 ; and from these a judgment may be formed
of the degree of accuracy attainable. It will be found that, while
T2
264 Mr. M. Ponton on certain Laws
tlic two sets agree very closely, this agreement does not extend
beyond the fourth place of decimals ; so that in no case can the
fifth and sixth places of decimals, as given by observation, be
depended on, while it is needful to carry the indices to the sixth
place of decimals in order to their fulfilling with exactness the
exponential law. But if the observed indices be correct down to
the fourth place of decimals, the exponential law, in combination
with the laws governing the extrusions, may be relied on for the
fifth and sixth places.
It is proposed, then, to consider all those observations in
which, when tested by these laws, no individual error amounts
to 0"0001, as of the first order, greater accuracy of observation
being unattainable; those in which no individual error amounts
to 0'0002, as of the second order ; tliose in which no individual
error amounts to 0'0003, as of the third order, and so on.
As regards Fraunhofer^s observations, it will be found that, of
the whole twelve, there are of the first order seven ; namely,
water (two sets), solution of potash, oil of turpentine, and three
specimens of crown-glass; while there are of the second order
five, all of them on fiint- glass.
With respect to Rudbei'g's ten observations on doubly-refract-
ing media, there are of the first order seven, namely, topaz
2nd axis, quartz ex. ray; Arragonite 1st axis, quartz 0. ray;
topaz 3rd axis, calc-spar 0. ray; topaz 1st axis: and of the
second order three, namely, Arragonite 3rd axis, calc-spar ex.
ray, and Arragonite 2nd axis.
With Powell's observations the results are not so satisfactory ;
but that the discrepancies which they present are due, not to any
peculiarity in the media, nor to any defect in the exponential law,
but simply to the inaccuracy of the observations themselves, may
be clearly shown. It fortunately happens that we have a set of
observations by Powell on water, on which we have two sets by
Praunhofer. While the two latter agree very closely with each
other, and quite as closely with the exponential law, both being
of the first order, those of Powell are so inaccurate that they can
be classed only as of the eighth order. Now this difference can
be attributed to no other cause whatever than to the inferior
accuracy of Powell's observations ; for it appears highly impro-
bable that it should be due to the difference of temperature at
which the observations were made. In the case of solution of
potash, on which we have also observations both by Fraunhofer
and Powell, and at temperatures more widely apart, the difference
in quality between the two sets is much less marked; for while
those of Fraunhofer are of the first order, those of Powell arc
of the second.
But if in so simple a case as that of water the observations of
of Chromatic Dispersion. 265
Jewell are so very inferior to those of Fraunhofer, it should not
occasion surprise to find that in some instances this inferiority is
still more marked, and that some of Powell's observations, when
tested by the exponential law, should be classed as only of the
tenth order. Of this we have an example in the case of nitrate
of potash, which is of low dispersive power, and should therefore
have presented no peculiar difficulties. But this case belongs to
a class of observations of which the observer himself says, that
the media being of low dispersive power, and considered by him
of little importance, the calculations were in consequence carried
to only a slight degree of approximation. So far, then, from
the discrepancies, in the case of nitrate of potash, tending to
shake confidence in the exponential law of the indices, they
ought to be regarded as strengthening its probabihty, by show-
ing it to be capable of detecting the errors in these observations
which might otherwise have escaped notice, seeing that, in con-
formity with the observed indices, nitrate of potash belongs to
the class of regular media ; and there is no other test by which
the errors could have been brought to light.
This example shows that, with reference to any general law of
dispersion, no medium ought to be viewed as of small import-
ance, but that the same attention should be given to secure
accuracy in media of low, as in those of high dispersive power.
Of the twenty-nine observations by Powell which have been
tested by the exponential law^ of the indices, there is not one
that can be classed as of the first order — a fact sufficiently indi-
cative of their general inferiority. There are, however, thirteen,
or nearly one-half, which are of the second order, and may there-
fore be regarded as fair observations. These are —
Sulphate of magnesia.
Solution of potash.
Sulphate of soda.
Alcohol.
Nitrate of bismuth.
Nitrate of lead.
Subacetate of V ad.
Muriate of ammonia.
Superacetate of lead.
Nitric acid.
Oil of sassafras.
Oil of anise, T. 13°-25.
and the same at temp. 20°'9. There are five of the third order,
muriatic acid, nitrate of mercury, nmriate of lime, rock-salt, and
oil of anise, temp. 15°"8. There are two of the fourth order —
sul])huric acid and creosote ; three of the fifth order — pyrolig-
neous acid, bisulphuret of carbon, and muriate of baryta ; one of
the sixth order — oil of cassia, temp. 11°; two of the seventh
order — solution of soda, and oil of cassia, temp. 10'; one of
the eighth order — water, temp. 15°*8; one of the ninth order
— oil of cassia, temp. 2.2°"5 ; and one of the tenth order — solu-
tion of nitrate of potash. From this enumeration it is clear
that there is no connexion l)ctwccn the amount of error ami the
dispersive power of the medium, seeing we have media of imv
266 Mr. jM. Ponton on certain Laws
aiul liiirh dispersive power indifferently aiuoiig the best and the
worst cases.
In the three sets of observations, there are fourteen of the first
order, in which the agreement with the exponential law may be
considered perfect ; and there are twenty-one of the second order,
in which the agreement may be regarded as nearly complete.
These together amount to thirty-five out of the fifty-one, or better
than two-thirds of the whole. To these may be added the five
of the third order, in which the agreement may be considered fair,
thus making four-fifths of the whole, in which the observed and
calculated indices agree as nearly as can be reasonably expected.
The whole errors in Fraunhofer's twelve observations amount
to 0-003-i49, or 0-000287 per medium, and 0-000041 per line.
In lludberg's ten observations, the sum total of the errors is
0-003204, or 0000320 per medium, or 0-000046 per line, so
that these two sets are nearly equal in quahty. In Powell's
twenty-nine observations, the total errors amount to 0-034400,
or about 0-001180 per medium, and 0-000170 per line ; so that,
in general accuracy, Fraunhofer's observations are to Powell's
nearly in the ratio of 4 to 1.
That the whole of the discrepancies between the observed in-
dices and those calculated by the exponential law are due, not to
any defect or' inaccuracy in that law, but solely to inaccuracies
in the observations, it is not difficult to show. As regards the
fourteen observations of the first order, there can be no doubt
whatever. With respect to those of the second order, it fortu-
7iately happens that the two sets of observations on oil of anise,
at temp. 13"-25 and temp. 20°-9, are both of this order, and
agree very nearly, — the cumulo eiTors in the former being
0-000393, and in the latter 0000387. But the observations on
the same medium, at the intermediate temperature 15^-1, are of
only the third order, — the cumulo errors being 0-000748, about
double of those in the former cases. Now this difference can arise
from no other cause than a difference in the degree of accuracy
with which the observations were made; so that there is here a
difference in the amount of error, arising simply from an inferior
degree of accuracy in the observations, equal to the total amount
of error in the two best observations on oil of anise, thus show-
ing that these latter errors must themselves be due to defective
observation. But it is equally clear that the greater eri'ors in
the worst set must also arise from inaccurate observations ; for
had these been made with the same care as the two first, they
would have been of the same quality. It may hence be fairly
infen-ed, that in all the observations, thirtj^-seven in number, in
which the cumulo differences do not exceed 0-000748, these are
due to inc«»rrect observations.
of Chromatic Dispersion. 267
Among the fourteen media in which the discrepancies are
greater, there is found water, as observed by Powell, in which
the total errors amount to no less than 0*001916j whereas in
Eraunhofer's two sets of observations on this medium, their
amounts are 0-00015 t and 0000205, — Powell's discrepancies
exceeding the least of Fraunhofer^s by 0*001762, an excess which
can be due to nothing but a difference in the degree of accuracy
with which the observations were made. Thus the total discre-
pancies of 0"001916 in Powell's observations on water are clearly
traceable to experimental inaccuracy. But the total discrepan-
cies in the case of Powell's observations on oil of cassia, temp.
14°, very little exceed this amount, being 0-001984; so that
these may also be fairly attributed to the same cause. Now the
reasoning applicable in the case of the oil of anise applies equally
to the observations on oil of cassia at temp. 10^ and temp.
22°-5. The discrepancies in these two cases amount respectively
to 0-003750 and 0-003529, or not far from double of what they
are at the intermediate temperature 14^. This difference can be
attributed to nothing but the inferior accuracy with which the
observations at temp. 10° and temj). 22°-5 were made ; and had
only the same amount of care been bestowed on these as on those
made at temp. 14°, the gross amount of discrepancies would not
have exceeded those presented in the latter case, which have
already been shown to be due to experimental error. Thus the
extreme amount of the discrepancies in the case of oil of cassia,
temp. 10°, maybe logically traced to defective observation; and
these discrei)ancies being the greatest in the Table, it may hence
be quite fairly inferred that all those of low^er amount ought to
be attributed to the same cause.
The indices, calculated by the exponential law from the four-
teen observations of the first order, may be regarded as being
quite as correct as they can be possibly obtained. Those calcu-
lated from the twenty-one observations of the second order may
be deemed very nearly correct ; while those calculated from the
live observations of the third order may be viewed as fair ap-
proximations to the truth. It is, however, too much to expect
of the exponential law that it should yield accurate indices from
the eleven observations of an order inferior to the third. No
mathematical law whatever can bring forth accurate results from
incorrect observations where the errors exceed a certain limit ;
the utmost that can be ex|)ected in such a case is, that the law
should indicate the probable position and amount of the errors of
observation, and exhibit the necessity for more careful repetition.
It is in this light, then, that the calculated indices of these eleven
cases ought to be regarded.
This point must be kept in view in examining the question,
268 Mr. M. Ponton on certain Laws
how far tlie peculiarities observed in some of the media^ as
respects the number and position of the nodes of the extrusions,
may be traceable to errors of observation.
In the case of sulphuric acid, these peculiarities are removed
by the entire extinction of the extrusions, under the operation of
the exponential law. But the extrusions are brought to assume,
by virtue of this law, the regular type in the following cases, in
which the observed indices cause them to appear quite irregular,
namely, muriatic acid, alcohol, solution of soda, pyroligneous
acid, and oil of anise, temp. 15°. See end of Table IV., where
the extrusions of these media are given as they appear after the
indices have been corrected by the exponential law.
The removal of the irregularity in the extrusions, by the ope-
ration of this law, is particularly noticeable in the case of oil of
anise ; for there is thus made to disappear from this medium the
apparent anomaly of its having its extrusions regular at temp.
13^'25 and temp. 20°"9, but irregular at temp. 15^*1, they being
thus rendered regular at all the three temperatures.
It is interesting to note in this ])articular case the effect of the
exponential law on the values of e, the index of elasticity, as
viewed in relation to the temperature. These values become —
Diff.
Temp. 13°-25 e = 1-478427 . . 1044
„ lo--l 1-477383 . . 3898
„ 20°-9 1-473485 . . 4942
These differences are not far from being proportional to the
differences of temperature, but they may be brought into that
precise ratio by a further slight alteration on the indices of refrac-
tion, while these latter may be at the same time preserved obe-
dient to the exponential law. This end may be attained by
making the values of log €„ and a^ stand thus : —
Temp. 13°-2o log e„ 0-1857298 o^ 0-006160,
Temp. 15°-1 log e„ 0-1857412 fl„ 0006303,
and Temp. 20°-9 log e„ 0-1847219 fl„ 0006350.
The values of e then become
Diff.
Temp. 13° 25 6 1-478482 . . 1181
„ 15°-1 1-477301 . . 3733
„ 20°-9 1-473568 . . 4914
These differences are in exact proportion to the differences of
temperature, while the values of e themselves are in the inverse
order of the temperature, thus strictly fulfilling the law.
The indices of refraction thus corrected will be found at the
of Chromatic Dispersion. 269
end of Tabic VI., and may be regarded as more accurate than
those calculated from the exponential law alone. It thus appears
that when observations are made at more than two different tem-
peratures and with sufHcient accuracy, they furnish data whence
the indices of refraction may be calculated so as to fulfil all those
three laws, namely, the exponential law, the law of regular ex-
trusions, and the law of temperature, as affecting the index of
elasticity. When the indices of refraction fulfil these three con-
ditions, they may be regarded as nearly quite correct.
In reference to the law of temperature, it will of course be
understood that it is the differences of expansion under the in-
fluence of temperature, rather than the differences of the degrees
of temperature themselves, to which the differences in the value
of the index of elasticity must correspond.
To the effects of the exponential law, in bringing the extrusions
into conformity with the regular type, a solitary exception is
presented in the case of the oil of cassia. The singleness of this
exception, however, raises a strong presumption that all media
whatever conform to the same regular type as respects their ex-
trusions, and that the apparent departure in the case of the oil
of cassia is due solely to errors of observation. This is rendered
the more probable by the fact of the proved existence of large
errors in the observed indices of this medium ; by the anomaly
that, at the intermediate temperature, it has a higher exponent
than at the higher and lower temperatures ; and by the circum-
stance that the corrections deducible from the exponential law
tend greatly to reduce, though not quite to remove, the irre-
gularity in the extrusion of G, in which the departure of this
medium from the regular type consists.
It would not be difficult to find for the oil of cassia a set of
indices of refraction which, while fulfilling the exponential law,
should at the same time render the extrusions regular, and also
fulfil the law of temperature as respects the index of elasticity,
taking advantage for this purj)ose of the analogies furnished by
the oil of anise*. Owing, however, to the inherent inaccuracy
* There seems to be some intimate connexion between the value of n,
the exponent of least extrusion, and the j)osition assumed by the nodes of
the extrusions with the tirst powers of the normals. Thus, in the case of
the oil of cassia, when the value of n is 3'4 or 35, the position of the lower
node is considerably on the II side of G. lint if the exponent be gradu-
ally lowered, the node will remove further and further from II, until, when
the value of n is 2!'. the node nearly coincides with G itself. lUit when
the exponent is still further reduced, the position of the node ^^radually
advances towards F, and the extrusions then present the re>:;ular type.
This is a point which invites fuither investigation; but for this purpose it
Avould be needful to have a nu)re accurate set of observations on oil of
cassia.
There seems to be also some probability that the positicm of the upper
270 Mr. M. Ponton on certain Laws
of the observations on oil of cassia, those indices coukl be regarded
only as approximations to the truth ; and such a result would
hardly justify detention from a more important branch of this
inquiry, namely, the institution of a comparison between the laws
brought to light by the foregoing investigation, and the well-
known hypothesis of M. Cauchy.
Suffice it meanwhile to have shown the high probability that
in every case the extrusions and the laws governing them are of
one uniform character, — a circumstance adding greatly to their
interest and their importance as one of the means available for
checking the accuracy of the indices, seeing that any departure
from this normal type may be regarded as a very strong pre-
sumption of inaccuracy in the indices.
It remains, then, to compare the results obtained from the
exponential law of the indices with those deducible from the
hypothesis of M. Cauchy, "that the differences between the
refractive indices of the medium are to each other very nearly as
the differences between the reciprocals of the squares of the
normal wave-lengths; or the refractive indices are each com-
posed of two terms, whereof one is constant for the medium and
temperature, tlie other reciprocally proportional to the squares
of the normal wave-lengths."
It is on the basis of this law that the indices in Powell's
Tables have been calculated. Those of the three lines B, F, and
H are assumed from observation ; and those of the four lines C,
D, E, and G are thence calculated by means of formulae based
on the above law.
In order to exhibit more perfectly the differences between the
results thus obtained and those derived from the law of a variable
exponent, whose value depends on the proportion which the
irrationality bears to the dispersion, the indices, as calculated
from the law of M. Cauchy, are given in Table IX., being ex-
tracted from Powell's Tables ; and the sums of the errors are
compared with those arising under the exponential law.
Fully to appreciate the superiority of the latter, it is well to
select a case in which the law of M. Cauchy wholly breaks down.
For this purpose the highly dispersive medium, bisulphuret of
carbon, will suffice. In this medium, the discrepancies arising
under the law of M. Cauchy, between the observed and the cal-
culated indices for the four lines C, D, E, and G, are
mC_0000800, '"D-0-001700, f^E -0-002000, ''GO'004400, S+0-008900.
The discrcj)ancies arising on the seven lines under the exponen-
node between C and D may be found to coincide witli that of the mean
wave M, whose refractive index is tliat for white light ; but this, too, is a
I'oint requiring further research.
o/ Chromatic Dispersion. 271
tial law, the exponent for this medium being 2o, are
'^B-l- 00001 13, '^C-0000252, '*D+0000047, '^E-OOOOllO, '^F-0-000295,
^G-0-000439, f^H+OOOOSW, S+0001675.
So that the sum total of these latter is less than the amount of the
single error in D in the former case, and less than a fifth of the
total errors arising under the law of M. Cauchy ; consequently, in
this important medium, the ratio in favour of the exponential law,
as compared with that of M. Cauchy, is more than 5 to 1. The
difference is still more striking if the individual discrepancies be
compared, — the highest arising under the exponential law being
only a tenth of that arising under Cauchy's law, the latter tlis-
crepancy, moreover, being far too large to be attributed to errors
of observation ; while those arising under the exponential law
are all of such moderate magnitude, that there can be no hesita-
tion in ascribing them to that cause.
From an inspection of Table IX. it will be seen that, as respects
Fraunhofei-^s observations, the agreement between the calculated
and observed indices is as 2 to 1 in favour of the exponential
law*. In Rudberg^s observations the ratio is as 4 to 3, and in
Powell's as 10 to 7, while from the three sets combined it is as
6 to 4. But the best criterion of judgment is furnished by those
media which have a high dispersive and extrusive power, and in
which the law of M. Cauchy entirely fails, presenting discrepancies
far too great to be attributed to experimental error. Such are
those in the case of the bisulphuret of carbon above noted ; such
are also the large discrepancies in the ease of the oil of cassia,
ranging between 0-0017 and 0-0029, while the largest indivi-
dual discrepancy arising under the exponential law is under 0-001 .
In some few instances it will be observed that the result appears
to be in favour of the law of M. Cauchy, but these anomalies are
all clearly traceable to experimental error. Looking at the
results as a whole, there can be no doubt that the decided supe-
riority rests with the exponential law, as being the true law of the
indices.
The great defect in the hypothesis of M. Cauchy is its failure
to accommodate itself to the pha^nomenon of irrationality and the
attendant extrusion of the fixed lines. Its apparent agreement
with observation in a considerable number of cases, arises simply
from the circumstance that, with the squares of the normals, the
extrusions are in those cases so small that they may be elimi-
nated without greatly atFecting the indices ; and it is only when
* It must be kept iu view, in examining this Table, that the normals on
which Pinvell's caleulations are based differ slii^htlv from those s]icciticd in
this paper ; but this circumstaucc docs not materially ati'eet the general
results.
272 ^Iv- G. B. J crrsivd's Remarks on
the dispersive and extrusive powers of the medium are large
that its inappHcabihty becomes manifest.
The exponential law, on the other hand, entirely overcomes
the difficulty arising out of the irrationality; because it shows
that in each medium there is, dependent on the proportion which
the irrationality bears to the dispersive power, a certain exponent
for the normals at which the extrusions attending the irrationality
are reduced to a minimum, and that with this exponent the in-
dices may always be obtained from two constants, — each index
being then reduced to two terms, one of which, e„, is constant
for the medium temperature and exponent; while the other {a„)
corresponds to a further shortening of the wave-length within
the medium, which is constant for each wave, and so inversely
proportional to the primary wave-lengths of the normals, with
this particular exponent applied to them, the formula for each
A,"
index being fi^rj. *•
A,
— —a„
e„
[To be coutinucil.]
XXXV. Remarks on Mr. Harley's paper on Quintics.
By G. B. JERRARDf.
IN the * Quarterly Journal of Pure and Applied Mathematics '
for last January, there is a paper by Mr. Harley " On the
Theory of Quintics,'^ respecting which I am induced to offer a
few remarks.
1. On comparing the results at which he has arrived,
/64-5QE^2^/{E(E3-108Q^)}.^-5Q'*=0, . (a),)
in his explanation of Mr. Cockle^s ' Method of Symmetric Pro-
ducts,* we may easily perceive (for Q, E are the coefficients of
the trinomial equation in x with which he sets out) that the
method in question is in general not applicable to equations of
the fifth degree.
For as the equation (coj) belongs, according to art. 8 of Mr.
Harley's paper, to a class of equations of the sixth degree, solved
by Abel, the roots of which, as is well known, do not involve
any radical higher than a cubic, it is manifest, from (w^), tliat
* Tlie refractive index of any medium at a given temperature, for irhite
light, may be found very accurately from the above fornuila by making
X=:0'93;:il!M, the length of the mean wave, in relation to that correspond-
ing to the fixed line H as luiity.
t Communicated bv the Author.
Mr. Harley's paper on Quintics. 273
the roots of the trinomial equation also must, if there be no error
in the processes, admit of being expressed by means of radicals
characterized by the symbols y^, 1/ only, that is to say, without
the aid of any function of the form \^z. And in effecting the
reduction of the general equation to the trinomial one, no such
function is introduced.
The method, therefore, even should it be found to extend
beyond the extreme case of .^, = 0, x^=^0, . .x^=.Q, cannot be
applied except when ^z (I mean an irreducible radical of that
form) does not enter into the expressions for the roots.
2. Postsci'ipt. — Since writing these lines, I have seen a paper
by Mr. Cockle in the Philosophical iMagazine for the present
month. The objection which attaches to his method from the
absence of quintic surds is not overlooked. But, instead of con-
fining himself to the elucidation of the origin of an error, the
existence of which is so obvious, he goes on to infer, from the
failure of his method, the impossibility of effecting, except in a
limited number of cases, the algebraical resolution of equations
of the fifth degree, — a result in the accuracy of which 1 cannot
concur. It is true that all methods of solution, if equally general,
must ultimately coincide. The success of one involves the suc-
cess of all*. The failure of one the failure of all. It is, how-
ever, far otherwise with respect to methods subject to conditions
not necessarily, or rather not universally, inherent in the subject.
3. But I come to what Mr. Cockle brings forward as his
weightiest objection to my method. He says, "The error of
Mr. Jerrard inheres, in my opinion, in his mode of comparing
the equations (ab) and (ac) at pages 80 and 81 of his most
valuable 'Essay.' His functions ,H, gE, ^, and 45 in art. 104
are foreign to the question, mere instruments for eliminating
radicalities. They lead to no other result than that to which the
immediate comparison of (ac) and
would conduct us, viz. an expression for H into which P/(/3,)
enters irrationally/' Doubtless the result in both cases would
be the same. On substituting the expression for qH in (ac) we
should find by the evanescence of N3, Ng, N,, Nq that
* See applications II. III. at pp. 84, 85 of my ' Essay 011 the Resolution
ofEquations,' published by Taylor and Francis, Red Lion Court. Fleet
Street, Loudon.
274 Archdeacon Pi-att on the Solidity and
just as before. The irrationality is merely one of form*. What
then ? In the place of an objection to my method, has sprung
up a vcriiicatiou of it.
All Mr. Cockle's other objections tend, in like manner, by
their failure, only to make more palpable the validity of the
method to which they are opposed. But of these hereafter.
March 1860.
XXXVI. Is the Problem, " How far is the mass of the earth solid
and how far fluid t" excluded from the domain of positive
Science ? By the Venerable John Henry Pratt, Arch-
deacon of Calcutta.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
rr^HE question I have placed at the head of this paper. Prof.
JL Haughton has answered in the affirmative in his paper in
the Transactions of the Royal Irish Academy, vol. xxii. p. 251,
" On the Original and Actual Fluidity of the Earth and Planets."
If this conclusion be correct, it must render altogether useless
such investigations as that by Mr. Hoi)kins regarding the thick-
ness of the earth's crust. This consideration invests Professor
Haughton's conclusion with so much importance, that it demands
attentive examination. It was upon this ground that I pointed
out in your Number for May 1859, what I conceived to be — and
still conceive to be — a fallacy in the reasoning which brought out
this conclusion. In his last paper, in your Number for December,
which reached me yesterday. Professor Haughton does not, in my
view, clear away the difficulty.
2. In his original communication to the Irish Academy he
deduces the following equation (I here use his own notation) : —
and by differentiation obtains from it
d^e 2pa^ de Ce/ P^_\_n (\'\\
da^^y^pct'da aA' ^pa^l ^ ^
Two lines further on he states that this is "independent of
the law of density and ellipticity of the solid parts of the earth."
* At the time of writing art. 104 of my ' Essay,' this second mode of
arriving at the equation
S/-r{P/(i..5)}=0
presented itself to my mind. But I did not like to deviate too widely from
the route I had taken in 1845.
Fluidity of (he Mass of the Earth. 275
It is this last statement whicli I controvert. In my paper
in your Number for May last (page 329, line 23), I assert that
equation (13) "assumes that the law of density and cllipticity is
continuous throughout the whole mass, solid and Huid, the solid
])arts lying in strata of the form and density they would have if
they were wholly fluid."
3. Professor Haughton, in your Number now received, replies
to my reasoning by showing that he has differentiated equa-
tion (12) right. This I never called in question. "The ques-
tion at issue" between us is not, as his "mathematical friend"
states, " to determine a rule for differentiating this equation
[viz. (12)] with regard to </." What I assert is, that certain
terms of the differentiated equation will not cancel each other
so as to pi'oduce equation (13), unless we make such an assump-
tion as involves this principle, — That the same law of density
and ellipticity belongs to the solid and fluid parts. This I will
now show more fully.
4. I would first, however, observe that equations (12), (13)
apply equally to the solid and fluid portions of the mass. Equation
(12) expresses the law, that the resultant of all the forces acting
on any particle is at right angles to the layer or sui'face in which
the particle lies. This law is essential to the equilibrium of the
fluid part. It is also tacitly taken to be true for the solid parts
by Professor Haughton. For he differentiates equation (12)
with respect to a, and therefore assumes that equation (12) holds
at the immediate neighbourhood, on both sides, of the surface to
which a belongs. In the case in which this surface is the
bounding surface between the solid and fluid parts, the mass is
solid on one side and fluid on the other. Hence equation (12)
applies to both the solid and fluid portions.
5. To banish the integrals from equation (12) and obtain
equation (13), we must multi])ly by a^, differentiate with respect
to a, divide by a'^, and differentiate again. The result is equa-
tion (13). The first differentiation produces, from the second
de de
term, a term — jpf'^j- ; and, from the third term, a term + ^pa^ --j-.
It is assumed that these terms cancel each other. So also the
second differentiation produces, from the second term, a term
+ P-T-: and, from the third term, a term +p-r- These are
da' ' . de^^
assumed to be equal to each other ; that is, p -5- is assumed to
have the same value on hoth sides of the surface of which a is the
mean radius. This will be the case when this surface is one of
the layers wholly within the fluid, or wholly within the solid
part, even though the laws of density and ellipticity of the fluid
276 On the Solidity and Fluidity of the Mass of the Earth.
and solid parts are different. But it will not be the case at the
bounding surface between the solid and tiuid parts, unless the
values of p-y-, derived from the law of the fluid and from the law
da
of the solid layers, are the same at this bounding surface. Asp
is some function of a, e is some function of a (as equation (13)
de
shows) ; hence p ;t- is some function of p only. Hence, then,
the laws of density of the solid and fluid layers may be diff'erent, as
far as the reasoning at present has carried us ; but the two laws
must give the same amount of density at the bounding surface,
otherwise equation (13) does not follow from equation (12).
6. Thus far, then, this is the result we are come to. The
mass consists of solid layers following a certain law of density,
and of fluid layers following the same or another law of density ;
but at the surface where they meet the density is the same.
Also the resultant force acting at any point of any layer, solid
or fluid, is at right angles to that layer.
7. Now the equilibrium of this mass will not be disturbed if
the flrst solid layer, reckoning from the inner surface towards
the outer one, become fluid, retaining its density. For the den-
sity of that one layer accords with the fluid law, and the forces
acting on the layer are perpendicular to its surface.
Equation (13), therefore, holds for the bounding surface be-
tween the first and second solid layers only on the same terms
that it holds for the bounding surface between the solid and
fluid portions. From this it follows that the density of the second
solid layer must follow the fluid law, and so in succession with
all the rest ; and therefore the law of density of the solid and
fluid portions must be the same throughout the whole mass, if
equation (13) is a correct inference from equation (12).
8. This result appears to me to be a priori evident without
this proof. For Professor Haugbton will acknowledge that the
equilibrium of the fluid parts will hold, if the solid parts do fol-
low the law of the fluid parts. But if any different distribution
of the solid parts take place, their resultant attraction on the
fluid cannot possibly be the same as before on every particle of
the fluid. The conditions of equilibrium would therefore not
hold, and the equilibrium would become impossible without a
change.
9. With regard to the other subject touched upon in Pi'ofessor
Haughton^s last paper — the argument drawn from the Himma-
laya Mountains, and the Ocean south of India, in my paper in
your Number for November — T will simply make the following
observations.
M. Espenschied on Nitride of Selenium. %77
(1) The mountain mass must not be considered as one rigid
mass of rock without natural joints. The Himmalaya Moun-
tains are far too irregular in their structure, and too full of gigantic
cracks and joints in all directions to allow of our applying the
principle of the arch in the way Professor Haughton suggests.
Moreover, if the cross strain in his arch, of 500 miles span and
thickness of only one quarter of a mile at the spring, is not suffi-
cient to compress the materials of the rock, it will surely break
off angles, as I have mentioned in art. 2, p. 346 of the paper
alluded to, and a catastrophe would ensue.
(2) If Professor Haughton will not admit this, and still thinks
that the principles of the arch should be applied to the crust
under the Himmalayas, what will he say to the second part of
my paper, in which the upward effect of the ocean is considered ?
Here the arch cannot possibly act.
(3) Professor Haughton notices a mistake I made in omitting
a 2 in my calculation ; but he observes that, as it does not
seriously affect my result, he lays no stress upon it. This mis-
take (which also occurs, I fear, in a treatise on "Attraction,
Laplace's Coefficients, and the Figure of the Earth," which by
this time is, I suppose, published) I detected about a month ago,
when it was too late to correct it. The calculation, however, in
which it occurs is not to find the actual thickness of the crust,
as will be obvious to my readers, but only to show that it is very
thick. Where the mistake occurs in your Journal, the result I
bring out is that the thickness of the crust in the middle of the
mass and at the end is 581 and 576 miles; whereas if the mis-
take bad not occurred, it would have come out 581 and 570
miles, which not only does not affect my conclusion regarding
the great thickness seriously, but in fact not at aD.
Calcutta, January 21, 1860.
XXXVII. Chemical Notices from Foreign Journals, -By E. Atkin-
son, Ph.D., F.C.S., Teacher of Physical Science in Cheltenham
College.
[Continued from p. 216.J
ESPENSCHIED*, in a recent dissertation, has described a
compound of nitrogen and selenium obtained by the action of
ammoniacal gas on sublimed cliloride of selenium, SeCl-. The
action is so very violent that the ammoniacal gas must be diluted
with a large volume of hydrogen, and the vessel in which the
action takes place carefully cooled. The chloride gradually
becomes green, and ultimately changes into a brown mass, in-
* Licbig's Annalen, January ISfiO.
Phil. Mag. S. 4. Vol. 19. No. 127. April 1860, U
278 M. Ufcr on Nitride of Chromium.
creasing considerably in bulk. This mass is placed in water,
wherein it separates as a brick-red powder, which is collected on
a filter and dried over sulphuric acid.
By a blow or by friction, or by being heated, this substance
explodes with a loud report, forming clouds of selenium vapour.
It is not pure nitride of selenium, but contains an admixture of
"selenium. This latter can be dissolved out by digestion with
solution of cyanide of potassium, which leaves the nitride of sele-
nium unattacked.
Pure nitride of selenium is an orange-yellow powder which
undergoes no change at 150", but explodes at 200°. It is ex-
tremely explosive ; the smallest pressure causes a detonation. It
also explodes when placed in chlorine, or in hydrochloric acid.
It is dissolved by nitric acid with formation of ammonia and
selenious acid. By treatment with potass, ammonia is liberated,
and selenate and selenide of potassium formed. Hypochlorite of
soda converts it into selenate of soda, with liberation of hydrogen.
Heated with water in a sealed tube to 150° — 160°, it is completely
changed into ammonia, selenious acid, and pure selenium.
Espenschied's analyses did not give very concordant results.
The mean numbers obtained were, selenium 83'69, nitrogen
16-33, which corresponds pretty closely to Se^ N. The body,
however, most likely contains hydrogen, and the formula
Se«N3H = Se2NH + 2Se2N,
which Espenschied considers probable, requires selenium, 84*57;
nitrogen, 15'07; hydrogen, 0"36.
Experiments by Espenschied to obtain a corresponding tellu-
rium compound have not given the expected results. Chloride
of tellurium, TeCF, absorbs ammonia, forming a greenish-yellow
mass which is not deliquescent. It consists of TeCP-J-2NH^*.
Ufer hasSnvestigated nitride of chromium f. In preparing it
he tried several methods, but found none superior to Schrotter's,
which consists in passing ammoniacal gas over sesquichloride of
chromium heated to a high temperature. The violet chloride
gradually changes, becomes first dark green, and ultimately
black. Vapours of chloride of amuionium arc given off, and
when these cease to appear, the reaction is complete. At the
close of the experiment, as high a heat is required as the tube
will bear. The decomposition is thus expressed : —
Cr2CF + 4NH3=Cr2N-F3NH''Cl.
Sesquichloride Nitride
of chrotw ium , of chromium .
* Which might be written NH^Cl, NH^TeCl.
t Liebig's Annalen, December 1859.
M. Ufer on Nitride of Chromium. 279
Nitride of chromium contains some undccomposed sesqulchlo-
ride which cannot be removed completely by its being heated in
ammonia. Ufer pui'ified it by an application of an observation
of Peligot. That chemist found that a very small quantity of
protochloride of chromium can convert a large quantity of the
insoluble violet chloride into the soluble modification. Accord-
ingly by digesting the impure nitride with zinc and hydro-
chloric acid, the nascent hydrogen (which does not attack
the nitride) reduces a portion of the sesquichloride to proto-
chloride, which then renders the remainder soluble; by wash-
ing the residue with water, any sesquichloride is completely
removed.
Tlie best method of determining the chromium is to convert
the nitride into sesquioxide by heating it in oxygen. Ufer also
determined the chromium by fusing the nitride with carbonate of
soda and nitre^ and estimating the chromic acid thus formed by
obvious methods. The analyses gave as a mean result 79*1 per
cent, chromium, and 20*9 per cent, nitrogen j agreeing well with
the formula NCr^, which requires 79"3 chromium, and 20*8
nitrogen. Schrotter assigned to this substance the formula
N^ Cr'^. But it is probable that Schrotter's preparation con-
tained some undccomposed chloride. Ufer^s formula for nitride
of chromium is rendered probable, not only by his analysis, but
by the mode of its formation, which is further quite analogous
to the formation of nitride of boron from boracic acid and
ammonia.
Nitride of chromium is a black amorphous powder. It has
the remarkable property (which it shares with analogous com-
pounds of tungsten) of decomposing ammouiacal gas into its
constituents when passed over it at a high temperature ; and
in its preparation, towards the close of the operation, there is a
moment in which the smell of ammouiacal gas is no longer
perceived, but instead of it nitrogen and hydrogen gases
appear.
Nitride of chromium is a very permanent body. It is with
difficulty attacked by the strongest acids. Heated in the air, it
is converted into oxide of chromium. It is not attacked by fusing
caustic potash, nor by fused carbonate of soda ; but heated with
aqueous potash in a sealed tube to 190° it is converted into
chromatc, and when fused with nitre a deflagration takes place.
It is dissolved by alkaline hypochlorites with disengagement of
nitrogen gas.
"When gently heated in a current of chlorine, small explosions
at first take place, probably arising from the formation of some
U2
280 Prof. Wbhler on Aluminium-leaf.
chloride of nitrogen ; the greater part of the mass is converted
into violet sesquichloride of chromium, which volatilizes.
Cr^N + GCl = Cr^CP + NCR
Nitride of Sesquichloride Chloride of
chromium, of chromium, nitrogen.
By dry hydrochloric acid gas it is with difficulty decomposed at
a high temperature into sal-ammoniac and sesquichloride of
chromium,
Cr2N + 4IICl = NH4Cl + Cr2CR
When nitride of chromium, placed in a covered crucible and
covered with a layer of borax, is heated in a blast furnace, it is
converted into metallic chromium, a small residue of nitride of
chromium being left.
M. Degousse, a goldbeater in Paris, has succeeded* in pre-
paring aluminium in fine plates like gold or silver. The opera-
tion of beating is effected in the iisual manner, but it is neces-
sary that the reheating be more frequent ; the fire of a chauffer
is most suitable. Aluminium-leaf may replace silver in many
cases ; its white, though less brilliant, is more durable.
Wohlert has the following remarks on Degousse's leaf-alumi-
nium. It is readily combustible ; if held in the edge of a spirit-
lamp flame, it takes fire and burns with great brilliancy. It is
very thin ; a cubic inch only weiglis a milligramme. If a leaf of
it be pressed together, placed in a bulb and heated by means of
a spirit-lam]) in a current of oxygen, it burns instantaneously
with a dazzling lightning-like appearance. The resultant alu-
mina is fused, and as hard as corundum. Aluminium wire also
burns in oxygen like iron ; but the combustion does not proceed
far, for the next parts melt away before they have reached the
temperature of combustion. Aluminium in the compact form
does not decompose water, but the leaf, when placed in boiling
water, decomposes a sufficient quantity to enable the hydrogen
to be collected. The metal assumes at first a faint bronze sur-
face colour. After several hours^ boiling, the laminse become
partially translucent, that is, converted into alumina. If the
residue be treated with hydrochloric acid, the unoxidized metal
is dissolved, while the alumina remains undissolved.
Several of the noble metals, but more especially platinum in
the finely divided state, have the property of causing a disen-
gagement of oxygen when placed in solution of peroxide of
hydrogen. For this enigmatical phsenomenon SchonbeinJ sug-
gests an explanation based on the following reactions.
* Barreswill's R('pertoire de Chimie, October 1859.
t Liebig's Anna'.en, February 1860.
J PoggendorffV, Annalen, January 1860.
Action of Platinum-black on Peroxide of Hydrogen. 281
1. Guaiacum resin solution gives with free as well as com-
bined ozonized oxygen a very delicate blue colour, while the
active oxygen of peroxide of hydrogen and of the antozonides
are without action upon it. But when platinum-black is added
to a solution of guaiacum which contains peroxide of hydrogen,
an intense blue colour is formed.
2. Ether dissolves peroxide of hydrogen without being affected
by it, while free or combined ozonized oxygen at once renders it
acid. Now if an ethereal solution of peroxide, and which at
once gives an intense blue with chromic acid, be agitated with
platinum-black, it loses the property of giving a blue with
chromic acid, and soon has an acid reaction.
3. Peroxide of hydrogen decolorizes indigo solution very
slowly, while it is instantaneously decolorized by free or com-
bined ozonized oxygen. If, however, a mixture of indigo solu-
tion and peroxide of hydrogen be agitated with platinum-black,
the solution is rapidly decolorized.
Hence it appears that the 0 of the peroxide produces the
same actions as the 0 of ozonized oxygen. IMay it not then be
assumed that platinum can change the positively active oxygen
of the peroxide into the negatively active state, without making
any assumption as to how this is effected. On this assumption
the 0 of the peroxide in immediate contact with the platinum
becomes changed into negatively active oxygen, 0 ; this 0 would
neutralize a portion of 0 and form ordinary oxygen ; in other
words, the layers of peroxide next the platinum would form ordi-
nary oxygen and water. After this catalysis, the 0 of another
portion of peroxide in contact with the platinum would be
changed into 0, which would decompose with another portion
of peroxide of hydrogen into water and oxygen, and so on. A
small quautity of platinum might thus decompose an indefinite
quantity of peroxide.
To saturate ether with peroxide of ethylc, Schonbein uses the
following method : — Dilute hydrochloric acid is added to a
gramme of peroxide of barium until the liquid is neutral ; the
mixture is then agitated with 40 grms. of pure ether and allowed
to stand. This etliercal solution, poured ofi" from the chloride of
barium, tux'ns chromic acid blue, decolorizes permanganate of
potash, and has iiulecd all the reactions of peroxide. It may be
distilled without alteration. When a volume of it is shaken with
four volumes of water, the peroxide of hydrogen is completely
removed. Potash removes it still more quickly.
Niepce de Saint-Victor and Corvisart* describe the following
instances of the peculiar influence which the sunlight exerts in
modifying and changing amylaceous substances.
* Comptes Rendus, September 5, 1859.
283 Action of Light on Amylaceous Substances.
If two 1 per cent, solutions of starch be prepared under the
same circumstances, and if one of them be kept in the dark and
the other exposed to the sunlight, the latter will be found to
exert an action on the polarizing apparatus ; more dextrine and
sugar have been formed. If very weak solutions be taken (about
20V0) ^^^^ exposed to the sunlight for about eighteen hours, it
will be found that the solution has lost the properties of the
original amylum, and more resembles inuline.
Many substances, such as lactate or citrate of iron, and cor-
rosive sublimate, limit or neutralize this action of the light;
while other substances, such as potassio-tartrate of iron, or nitrate
of uranium, greatly increase it.
Dextrine and cane-sugar are unaffected by light.
There is a curious action on oxalic acid. If a 4 per cent, so-
lution of the acid be mixed with a 1 per cent, solution of nitrate
of uranium, and the mixture boiled for even a considerable length
of time, pi'ovided this is done in the dark, no change takes place.
But if the light, even of a clouded sky, have but a momentary
action, a decomposition, evidenced by the disengagement of gas,
at once sets in ; and if the mixture be placed in the sun, a quan-
tity of carbonic oxide may be collected. That this action is due
neither to the temperature nor to the free acid, is evident from
the fact that at a temperature of zero, and with the employment
of oxide of uranium, the same results are obtained.
Direct experiments have shown that animal starch (glyco-
genous substances) is more rapidly changed into sugar in the
light than in the dark ; and, remarkably enough, nitrate of ura-
nium decreases instead of increases the action.
It is remarkable that animal starch in frogs* liver is not
changed into sugar in winter, which is also the case with the
vegetable starch.
This might explain why the sugar-forming substances which
are so abundant in the membrane of the foetus immediately
disappear after birth.
It can scarcely be doubted that light plays a slow but very
powerful part in effecting changes in the animal body ; and it is
evident that a knowledge of the substances which accelerate or
lesson this action is of great importance in medicine. Th
symptoms of diabetes, and the action which light has been ob-
served to exert on scrofulous persons, may be adduced as cases
in point.
M. Cloez has described* two new benzoic compounds. ^^Tien
cyanate of potash is mixed with chloride of bcnzoyle, and the
mixture heated to nearly the fusing-point of the cyanate in an
* Repertoire de Chimie, January 1860.
M. Cloez on Benzoic Compounds. 283
assay flask, carbonic acid is given off, and chloride of potassium
formed, with which remains associated a new body, ajaphenine.
Some bcnzonitryle is formed at the same time. Cyaphenine is
volatile without decomposition, and may therefore be separated
from the chloride by heat ; or the chloride may be dissolved out
by water.
Cyaphenine has the formula C'^^H'^N^; it corresponds to
cyanethine, C^^H^^N^, discovered by Frankland and Kolbc.
The latter body may be regarded as a triple molecule of cyanide
of ethyle, Ci8Hi^N3 = 3(C4 H^C^N) ; so cyanethine may be
considered as a triple molecule of benzonitrile or cyanide of phe-
nyle, C'^^W^^3 = S{C^^R^C'''^). The formation of cyaphe-
nine may be thus expressed : —
3C14H502, C1 + 3K0, C2NO = C^-Hi5N3 + 3KCl + 6C02.
Chloride of Cyanate of Cyaphenine.
benzoyle. potash.
Cyaphenine is a neutral, solid, hard substance, with a crystal-
line fracture; it fuses at 224°, and distils at 350°. It is little
soluble in absolute alcohol. Potash decomposes it, liberating
ammonia. Treated by strong nitric acid it yields a- crystallized
nitro-compound, C^^ H^^ ^-^Qy -^s^
Thiobenzoic Acid, C^* H^ 0- S, HS.— This body corresponds to
thioacetic acid, obtained by Kekule by the action of pentasul-
phide of phosphorus on acetic acid. It is prepared by adding
chloride of benzoyle to an alcoholic solution of hydrosulphide of
potassium. It crystallizes from bisuljjhide of carbon in rhomb-
oidal plates. When pure it is inodorous and tasteless. It fuses
at 120°, and begins to decompose at about 160° — 180°. It is
not soluble in water, and but slightly so in alcohol and in ether.
Its best solvents are sulphur compounds, such as mercaptan,
sulphide of ethyle, and bisulphide of carbon. It combines with
potash, soda, and ammonia to form definite crystallized salts,
from which the acid is liberated unchanged on the addition of
hydrochloric acid.
Kekule's thiacetic acid has been obtained by Jacquemin and
Vosselmann* by the gradual addition of chloride of acetyle to
hydrosulphide of potassium.
Carius, in a paper f on the equivalent substitution of oxygen
by sulphur, describes several new sulphur compounds.
The action of pentasulphide of phosphorus had been inter-
preted by Kekule as being analogous to that of pentachloride of
* Comptes Rendits, vol. xlix. p. 371.
t Liebig's Annalen, November 1859.
284 M. Carius on new Sulphur Compounds.
phosphorus, and as taking place in the following manner : —
5(GM16 0) + P^S^ = 5(GMI«S) + PH4^
Alcohol. Pentasulphide Mercaptan. Anhydrous
of phosphorus. phosphoric acid.
A careful study of the reaction has led Carius to a different con-
clusion. He tinds that sulphuretted hydrogen is constantly dis-
engaged, and that mercaptan is only obtained when the mixture
becomes much heated. Carius compares the reaction to that of
anhydrous phosphoric acid on alcohol, and expresses it by the
equation
5(€^H^G) + P^S^= 2IP.S+ ,^f, |03+,p?J|^3l0^S.
Alcohol. Pentasulphide ^^ ,'',-' J 7^ i ^
of phosphorus. New body. New body.
Both the new substances are formed in some quantity. The
first of them is an acid, which Carius names diet/ujlsu/jihophos-
phoric acid, and is diethylphosphoric acid in which the oxygen
of the radical phosphoryle is replaced by sulphur. It is a vis-
cous oily liquid, with a very sour and bitter taste. It is a stable
body, but when heated it decomposes with formation of mercap-
tan. It forms a series of well-defined salts. The lead and zinc
salts have the peculiarity of being precipitated in oily drops, and
of solidifying when touched with a hard body. The salts, like
the acid, arc inodorous.
The other body formed as above is disulphophosphate
PS'" "1 O'"*
of ethijle, //j|2 TT5N3 fa . It is a colourless oily liquid, with an
aromatic but somewhat alliaceous odour. By treatment with
hydrosulphide of potassium it yields the potassium salt of a new
acid, diethyldisulphojihosphoric acid and mercaptan. Thus,
P© \ O I TT-TTO _ PS 1 ^ ! PSUeCl
1^' , u \^ Hydrosulphide ^f ^f^. \. ^J^ ^^ Mercaptan.
Disulphophos- p'f potassium •L'lethyldisulphophos-
phate of ethyle. phate of potassium.
The action of mercaptan on disulphophosphate of ethyle is very
interesting as leading to the formation of mixed sulphur-ethers.
The formation of a mixed sulphur-ether of ethyle and methyle
takes place as follows : —
(GMiTj8 "^ Methyle- ~ (€^H^)^n/S +C2IP5/^-
Disulphophos- niercai)tan. Diethyldisulpho- New sulphur-
j)hate of eth}le. ' ' j)hosphoric acid. ether.
Carius has prepared the corresponding mixed sulphur-ethci*,
ns us f^i ^°^ w^^^ shortly describe it.
On Alloxan and new Derivatives. 285
By the action of pentasulphide of phosphorus on mercaptan,
or better on mercaptidc of mercury, Carius has obtained ieira-
sulphophospliate of ethijle, or phosphate of ethyle in which all
the oxygen is replaced by sulphur.
PS"' "1 PS'" ^
5(€Mi^HgS) + P2S-^=2Hs^S+,c2H5)2Hc. P'+ lQ^Y\^f \^^'
Mercaptideof ^^ TetVasulphophos-
"^^■^""■y- phate of ethyle.
Tetrasulphophosphate of ethyle is an oily, clear, yellow liquid,
which is very like disulphophosphatc of ethyle, but more de-
composable.
Alloxan, C^H^N^O^, and parabanic acid, C^H^N^O^, both
products of the oxidation of uric acid, exhibit a great analogy of
properties ; both are decomposed by alkalies in a similar man-
ner, and yield homologous products. By the action of reducing
bodies on alloxan, a substance, alloxantine, is formed. Lim-
pricht has found* that, by the action of nascent hydrogen on pa-
rabanic acid, a corresponding compound, oxalantine, is formed : —
Parabanic acid. Oxalantine.
It is prepared by adding dilute hydrochloric acid and zinc to a
solution of parabanic acid ; a slow disengagement of hydrogen
takes place, and a white crystalline compound of oxalantine and
zinc is formed. When this is treated with sulphuretted hydrogen,
and the solution evaporated, oxalantine is obtained in crystalline
crusts. It is little soluble in water, and almost insoluble in
alcohol and ether.
Alloxan, by the action of diflfereut cyanides, undergoes differ-
ent decompositions. When treated with cyanide of potassium, dia-
lurate of potash is formed ; but if cyanide of anmionium be used,
the result, as Rosing and Schischkoff have shownf, is diiferent.
They found that a new body, oxalan, to which they ascribed the
formula C^°IP^"N'*0^", was formed in the reaction. Liebig,
who had previously observed this reaction, examined the body J,
and found that the formation of oxalan might serve as a test for
the presence of alloxan in animal fluids. If to a liquid contain-
ing only a small quantity of alloxan, hydrocyanic acid and then
ammonia be added, a precipitate of oxalan is formed. Although
he did not propose a new formula for the body, he analysed it,
and pointed out that the ratio of the carbon to the nitrogen was
as 2 : 1 §.
Strecker has subsequently examined § the formation of oxalan,
* Liebig's Annalen, August 1859. f Ibid. vol. cvi. p. 255,
X Ibid, vol. cviii. p. 126. § Ibid. January 1860,
286 On Alloxan and new Derivatives.
and confirms the previous statements. In its formation the pro-
portion of hydrocyanic acid is immaterial; a very small quantity
can convert a large quantity of alloxan into oxalau. It takes
no part in the reaction, and merely serves as a sort of ferment.
It is known that hydrocyanic acid effects in a similar manner the
conversion of hydride of henzoyle into the polymeric benzoin.
When a tolerably concentrated solution of alloxan is used, dialu-
rate of ammonia is formed. Strecker's analyses give for oxalan
the formula C^ H^ W 0'^ ; and he expresses its formation thus :
witer! : ^{i:^g:l=CBH^N^O« Dialuric acid.
Ammonia. H^N ^^ ^^ Carbonic acid.
It may be regarded as the amide of oxaluric acid, oxaluramide.
By treatment with water it is resolved into oxalurate of ammonia,
a part of which is further decomposed into oxalic acid and urea.
C6 H5 W 06+2HO = NH4 0, C^ H^ N^ 0^.
Oxalan. Oxalurate of ammonia.
Compounds analogous to oxalan, but containing ethylc, methyle,
or pheuyie in the place of hydrogen, may be obtained by substi-
tuting in the preparation the corresponding amide base for
ammonia.
If to a solution of alloxan containing hydrocyanic acid, car-
bonate of potash is added to alkaline reaction, carbonic acid is
disengaged and dialuric acid separates, and the solution contains
oxalurate of potash. Thus,
2(C8H2N20«)+2HO+2KO=C«H3KN20HC6H3KN20H2C02
Alloxan. Dialurate of Oxalurate of
potash. potash.
Both in the case of the decomposition of alloxan by cyanide of
ammonium and by cyanide of potassium, the hydrogen of the
water changes part of the alloxan into dialuric acid, while the
oxygen oxidizes a like quantity into carbonic acid and parabanic
acid. In the presence of ammonia the parabanic acid forms
oxaluramide, in the presence of fixed alkalies an oxalurate.
Pui*e ferro- and ferri-cyanide of potassium have no action on
alloxan solution ; but if, as is frequently the case, they contain
traces of cyanide of potassium, oxaluramide is formed. A solu-
tion of alloxan might accordingly be used to detect the presence
of cyanide of potassium in ferro- or ferri-cyanide of potassium.
Strecker suggests, and will pursue the question, whether the
poisonous action of hydrocyanic acid on the blood of vertebrate
animals may not depend on its exerting a decomposing action
On Luminosity of Meteors from Solar Reflexion. 287
on the constituents of the blood similar to that seen in the case
of alloxan.
Riche* has investigated the decomposition of some bibasic
acids. When suberic acid is heated with excess of baryta, vapours
are given off which condense into a pale yellow liquid. On recti-
fying this, it is found to consist principally of a liquid which
boils at 76°, the analyses and vapour-density of which lead to
the formula C^^ H^'*. Its formation may be thus expressed : —
Ci6Hi2 06,2HO + 4BaO = Ci2?p4 + 4,BaOC02.
Suberic acid. Hydrocarbon.
It is a mobile, highly refracting liquid, of specific gravity 0'671.
It is converted by chlorine into a viscous mass with disengage-
ment of hydrochloric acid. With bromine, iodine, nitric acid,
and sulphuric acid no definite results are obtained.
Sebacic acid distilled with excess of baryta behaves in a similar
manner ; the reaction is very energetic, and it is necessary to mix
the mass with a quantity of sand. The liquid product, when
redistilled, consists of a hydrocarbon boiling at 127° C. It is a
colourless, highly aromatic lujuid, and burns with a blue-edged
flame. Treated with chlorine it becomes thick, and disengages
hydrochloric acid. Its analyses and vapour-density give for it
the formula C^^H'^. It appears to contain a little of the
body Ci«Hi«.
The formation of the hydrocarbon is thus :
C20Hi6 06,2HO + 4BaO = C'«HiH4BaOC02.
Sebacic acid. Hydiocavbon.
From their composition these hydrocarbons would belong to the
series of homologucs of marsh-gas, C* H" "''''. They are probably,
however, only isomeric. The hydrocarbon next below the one
from suberic acid, hydride of amylc C'^ IP'^, boils at 31°; while
the hydrocarbon, C^^ IV\ boils at 76°, and C" H'^ boils at 127°.
It is probable that this series of bibasic acids will yield a series
of hydrocarbons isomeric with those from the monobasic fatty
acids.
XXXVIII. On Luminosity/ of Meteors from Solar Reflexion.
By 11. P. Greg, F.G.S.-\
IT has as yet by no means been decided from what cause arises
the luminosity of shooting-stars. I do not now propose to
consider in detail all the various theories relative to this subject,
but shall endeavour to prove that their luminosity cannot at
least arise from solar reflexion, a theory partially supported by
* Comptes Rendus, vol. xlix. p. 304. Repertoire de Chiinie, Jan. 1860.
t Communicated by the Author.
288 Mr. R. P. Greg on Luminosity of Meteors
Sir J. Lubbock and others. The very sudden appearance and
disappearance of shooting-stars and small meteors, and their
general resemblance on a small scale to comets which shine
by solar reflexion, certainly favour the idea, either that suddenly
entering the cone of the earth's shadow they are instantly
eclipsed, or conversely, become visible as they emerge from it ;
or secondbj, previously self-luminous in planetary space, they
may become suddenly extinguished on entering the denser atmo-
sphere of the earth; or thirdly, they may suddenly become
visible and luminous, only on entering the earth's atmosphere by
friction and compression, by rapid absorption of oxygen and
sudden chemical action, or by electrical excitation.
I shall consider the first supposition most fully and in the
first instance, because I consider it may be most readily and
completely disproved. Sir J. Lubbock, in an interesting paper
in this Magazine for February 1848, and one that has since
been frequently referred to, considers the hypothesis of solar re-
flexion as a very applicable one in certain varieties of shooting-
stars : he even says, " knowing the time when, and the place
where the star disappeared, the elements of the geometry of three
dimensions furnish the means of determining the exact distance
of the body from the place of the spectator or from the centre
of the earth ;'^ and in his paper he gives several geometrical
equations and formulaj for assisting such determinations. I do
not propose entering into the nature of these calculations, or to
question either the results or the data, but merely by a different
treatment to show, if I can, how unlikely, if not impossible, it is
that ordinary shooting-stars (I mean, of course, those not show-
ing symptoms of active ignition within the lower limits of the
earth's atmosphere) can ever shine by reflected solar light ; and
this simply from the fact that they would be quite too far off for
us to observe such small bodies, at even the minhmmi distance
at which (at certain times and places on the earth's surface when
and where we know they are very frequently seen) they actually
could be so visible.
The problem I propose then to solve is, what is the minimum
distance at which a shooting-star could be thus visibly luminous
seen at an angle, say of 45 degrees above the horizon (the ma-
jority of shooting- stars appearing, as a rule, to the spectator
at even a greater angle), to an observer situate at midnight
within the tropics, or, to be more precise, at the equator, about
the time of the vernal or autumnal equinox.
In fig. 1, let S be the centre of the sun, and E that of the
earth, and S A and E C semi-diameters of sun and earth respect-
ively; let SE = 95,000,000 miles, BS and CE = 3950 miles,
and SA=423;500 miles; then supposing the shadow of the
from Solar Reflexion. 289
earth to form a true cone a 0 a', on the principle of similar tri-
angles we have the proportion
B A=418,550 : B C = 95,000,000 : : E C = 3950 : EO
=855,660 miles.
Fig. 1.
the length of the axis of the shadow from the centre of the earth.
And the diameters a a', b h\ &e. are in proportion to the distances
Qw, Ox, &c., as the diameter ?-r' = 7900 miles to the whole
length EO,&c. Now E C = E ?<; = 3950 miles ; andlet !^-a'=200
miles, then we have
855,660 : 7900 : : Oa; = 851,510 : 786.2 miles =hV ;
similarly, a a' = 7863^ miles; and calling z^r=: 8000 miles, we
have c?rf' = 7790 miles; andif?^-?/ = 3931, thence' = 7831 miles.
I have taken w x =200 miles, that heing considerably over
the average distance of shooting-stars whose distances have been
pretty accurately determined by Hciss, Brandes, Benzenburgh,
Twining, and Quetelet ; xo is the situation of the supposed ob-
server at midnight, near the equator at the time of the vernal or
autumnal equinox. From the above it will be seen that at a
distance of 8000 miles from the spectator at ?/', the cone of the
earth's shadow or umbra would have a breadth of not less than
7790 miles.
On referring now to fig. 2, which is merely a portion of fig. 1
enlarged for the sake of convenience, it will be easy to ascertain
the minimum distance w c at which a shooting-star m could be
visible outside the cone of shadow to a spectator at iv, the angle
aw 7/ being = 90^, and «ra = u'y=3931 miles; then as cy
7831 _.., .,
.-. wc= -/(39152-f 3931^) =5547-97 miles,
the angle mvc being consequently just over 45°, i. e. a distance,
290 On Luminosity of Meteors from Solar Reflexion.
as far as we kuovv, far too great to admit of our seeing ordinary
shooting-stars, at least in countries within the tropics, and if
shining by reflected solar hght.
Fig. 2.
The distance to the outside of the umbra in latitude 45° half-
way between w and r, as at v', would certainly be considerably
less than 5547 miles ; though this would not vitally affect the
question, as the distance towards c' would proportionately in-
crease ; and v^ a would still be over 1500 miles at midnight.
If the altitude of the meteor be, say 64P, dz being = ■
= 3895 miles, then 26't?=8900 miles; and if seen in the zenith
at 0, its distance would not be less than 871,710 miles, as seen
from ic, the supposed centre of the cone of shadow.
Now as the average distance of shooting-stars at the time of
their visibility is not much more than ] 00 miles, varying from
50 to 150 miles, and as we usually see them in all quarters of
the heavens at an average elevation of at least 40 degrees, it is
pretty clear, I think, if the preceding calculations and supposi-
tions are correct, that the majority of the shooting-stars we see
do not shine by reflected solar light.
I may at a future time ofl'er some observations on other and
more probable causes of luminosity in meteors and shooting-stars,
and in the mean time refer those interested in this subject to the
last Report of the British Association for Leeds in 1858, by
the Rev. Baden Powell. The theoiy of Mr. Daniel Vaughan,
alluded to in that Report, deserves attention.
[ 291 ]
XXXIX. On a Carbonate of Lead from Leaden Coffins. By
Richard V. Tusox, Lecturer on Chemistry at Charing Cross
Hospital*.
ABOUT twelve months ago an Order of Council was issued
directing the coffins in the vaults of the church of St. Mar-
tinis in the Fields to be transferred to the catacombs. A few
days after the appearance of this order, my friend and colleague
Mr. Canton, in company with several other gentlemen, visited
the vaults with the view of endeavouring to find the remains of
the late celebrated surgeon, John Hunter, which were known to
have been deposited there. The search proved successful, and
Hunter's remains were subsequently reinterred in Westminster
Abbey.
During his visit, Mr. Canton observed that many of the leaden
coffins, although they retained their original shape, were, with
the exception of an external and exceedingly thin plate or foil of
metal, converted into an earthy-looking substance. Several
pieces of this substance were removed from a coffin which, there
is good reason for believing, had been in the vaults about eighty
years. These were placed at my disposal ; and although it was
thought that they principally consisted of carbonate of lead, it
was nevertheless considered, from the peculiarity of the circum-
stances under which the material was formed, that the results of
its analysis might prove somewhat interesting.
The pieces of the substance referred to were about a quarter
of an inch in thickness : they had a laminated structure, and
possessed a fawnish or drab-white colour. Neither crystalline
form nor metallic lead were detected even by the aid of the
microscope. The material was tolerably brittle, and readily
reduced to an impalpable powder. On submitting it to quanti-
tative analysis, the following were the results obtained : —
Moisture 0*10
Organic matter and loss. 0'52
Peroxide of iron . . . 1"94
Protoxide of lead . . . 82-291 _ fPbO, CO^ 92-28
Carbonic acid . . . . 15-15 j ~ (^ -fPbO 5*10
100-00
The results of the analysis of this substance, therefore, show
that it chiefly consists of protocarbonate of lead with a small
proportion of anhydrous protoxide of the same metal. The pro-
duction of these compounds was doubtless mainly due to the
* Commuuicated by the Author.
29.2 Mr. R. Tuson on a Carbonate of Lead from Leaden Coffins,
moisture and carbonic acid evolved during the decay of the
animal remains, acting, conjointly with the oxygen of the air, on
the leaden coffins in which the bodies were placed.
If one might venture to assign a formula to this mixture of
carbonate and oxide of lead, its composition would be represented
by PbO + 15(PbO, CO^), as the following numbers clearly
indicate : —
Calculation. Experiment.
ir)PbO = 1785-6 . . 84-41 84-45
15C0'2 = 3300 . . 15-59 15-55
100-00 100-00
The interesting points in connexion with this substance are,
that it is anhydrous, that it contains but a small excess of oxide,
and that it consequently differs in composition from any of the
carbonates of lead hitherto described as being produced by the
united action of air and water on metallic lead ; or by the influ-
ences concerned in the well-known Dutch method for manufac-
turing " white lead,^' and which, it is believed, approximate in
character to those under which the material forming the subject
of this communication was developed.
The difference in composition of the various carbonates of lead
formed under the circumstances referred to, will be seen by
glancing at the subjoined Table : —
Source. Composition.
Air and water on lead . PbO, HO + PbO, CO^.
Dutch method . . . PbO, HO+2(PbO, CO^),
and sometimes
PbO, HO + 3(PbO, C02).
Leaden coffins. . . . PbO + 15(PbO, CO^).
Were any of these hydrated and basic carbonates of lead ex-
posed sufficiently long to the action of carbonic acid, they would
in all probability be transformed into perfectly neutral and anhy-
drous carbonates.
Lastly, it is most likely that the lead of the coffins was first
converted into hydrated oxide, then into hydrated and basic car-
bonate, and finally into the anhydrous carbonate of the compo-
sition already given.
March 21, 1860.
[ 293 ]
XL. On Osmious Acid, and the position of Osmium in the list of
Elements. By J. "\V. Mallet, Professor of Chemistry, &;c.,
University of Alabama^.
IN most chemical text-books it is stated, on the authority of
Berzelius, that there are five oxides of osmium — OsO,
Os^O^ OsO^, OsO^, and OsO"* — of which, however, the second
and fourth have not been isolated, although compounds containing
them are known. To these may be added a blue substance,
first obtained by Vauquelin and supposed by Berzelius to con-
sist of OsO united to either Os"^ 0^ or OsO'-, and the highest
oxide, probably OsO^, the existence of which was announced by
Fremy in 1854.
While preparing osmium from some black platinum residues,
I have accidentally obtained a substance which there is some
reason to believe may be osmious acid — the hitherto unisolated
teroxide — mixed indeed with osmic acid, but still permitting cer-
tain of its properties to be observed.
Three or four ounces of the platinum residue were treated by
a modification of the original process of Wollaston, now seldom
adopted. The powder was mixed with three times its weight of
nitre, the mixture was fused for some time in an iron crucible,
and then poured out upon an iron plate. While still warm the
fused cake was broken into fragments and put into a flask fitted
with a cork, through which passed a tube two feet long, bent at
right angles, and a funnel-tube, the latter drawn out to a very
small bore at the lower end, and reaching to the bottom of the
flask. The bent tube was well cooled, and , undiluted oil of
vitriol was very cautiously poured, by a few drops at a time, into
the funnel.
The acid produced intense heat on coming in contact with the
cake of potash salt, and oily drops of a bright yellow colour began
to make their appearance in the cooled tube. These drops very
slowly congealed to a solid resembling imblcachcd bees-wax.
By the time the sulphuric acid had been added in slight excess,
a considerable quantity of this yellow substance had collected
in the tube and in a receiver attached. By gently heating, the
whole was obtained in the receiver, and united under a little
water to a single mass. Towards the end of the distillation
colourless needles and fused drops of the well-known osmic acid
came over, and doubtless a considerable portion of the yellow
mass in the receiver consisted of the same.
At first it seemed probable that the yellow colour of the latter
was due merely to some impurity, and it was therefore cautiously
* From Silliman's American Journal for Januar}' 18G0.
Phil. Mag, S. 4. Vol. 19. No. 127. April 18G0. X
294 Prof. J. "VV. jNIallet on the Chemical and
resubliined, but it again collected of the same tint as before. It
appeared to be even more fusible and volatile than osmic acid ;
t took a long time to congeal under a stream of cold water flow-
ing over the outside of a tube in which it had been melted.
The water in which it was fused acquired a bright yellow
colour, and gave off fumes, the odour of which seemed to me
somewhat different from that of osmic acid, and which irritated
the eyes so insufferably that it was scarcely possible to finish
work with the acid and put it up for preservation. It was re-
moved as a single cake from the water, and sealed up hermeti-
cally in a glass tube which had been previously cleansed with
care from all traces of dust or other organic matter. The water
in which it had been fused was mixed with caustic potash, and
gave a solution of very dark brown-red colour, such a tint as
would probably result from a mixture of the red* osmite of pot-
ash discovered by Fremy with the orange-brown osmiate of pot-
ash.
The sealed tube containing the fused cake or stick of yellow
acid was allowed to remain upon a table exposed to the direct
rays of the sun. The acid immediately began to sublime upon
the sides of the tube, not in long needles and prismatic ciystals
hke osmic acid (which seems to be monoclinic), but in feathery
crusts like sal-ammoniac, which under a lens had somewhat the
appearance of minute octahedrons grouped together. The colour
was stdl bright yellow^, but in a short time the sublimed acid
began to turn black, and in twenty-four hours the whole inner
surface of the tube was perfectly black and opake. A tube
containing pure colourless osmic acid has been exposed in a simi-
lar way to the sun for three weeks without any such blackening
taking place. A tube closed by a cork, or one from which dust
has not been carefully removed, will often cause osmic acid to
turn dark, but never exhibits anything like the absolute black-
ness and opacity of the whole tube noticed in the present in-
stance.
It is easy, however, to imagine the cause of this change under-
gone by the yellow acid if it be in fact the teroxide of osmium
(mixed with osmic acid). The teroxide probably broke up into
osmic acid, and one of the lower oxides of osmium, or perhaps
the metal itself. We might have
20sO^= Os04-fOs02,
50s03=30sO*-fOs'-^03,
30s03=20sO'i-fOsO,
or 40s03=:30sO'' + Os.
* A rose-red coloiu- is also characteristic of the salt supposed bv Berze-
lius to he the ammonio-^ercA/or jc?e of osmium, corres})ondiug in the chlorine
series to osmite of ammonia.
Physical Relations of Osmium. 295
In order to ascertain, if ])ossible, which of the above changes
had taken place, the tube was opened two or three months after
it had been sealed, and the contents were examined. The fused
stick of acid was found to be black and partially friable; on
heating in another glass vessel, most of it sublimed, leaving a
little black powder behind, and condensed in needles, still
slightly yellowish, but differing little in appearance from com-
mon osmic acid. The inner surface of the original tube was
found coated with a thin, filmy, adherent crust, of a black colour
and considerable lustre. This was scraped off, and a portion of
it gently heated in a stream of dry carbonic acid gas until all
traces of adherent osmic acid were driven off. After cooling,
the carbonic acid was replaced by dry hydrogen, and heat was
again applied. Water condensed on the tube beyond the heated
part, thus proving that an oxide of osmium, not the metal, was
under examination. Replacing again the hydrogen by oxygen,
osmic acid was produced and carried off with the stream of gas.
The black powder scraped oft" from the original tube was heated
with hydrochloric acid, and seemed to be but slowly acted on ;
the acid, however, assumed a green colour, and hence it is pro-
bable that the osmium existed as protoxide.
It is not easy to see, without further investigation, how os-
mious acid could have replaced in part osmic acid in the attempt
to prepare the latter as above described. Is there a particular
stage of the decom])osition of nitre by heat at which osmium
may replace nitrogen in nitrite of potash (KO, NO^) ? From
the relations of the two elements, to be noticed presently, this
would seem probable, and in fact Fremy has noticed the crystal-
lization of osmite of potash from a solution in hot water of the
fused cake of nitre and iridosmium. A reason for osmic acid
(OsO'*) being usually obtained from the latter, instead of osniious
(OsO'^), might perhaps be found in the fact that the chemists
who of late years have worked upon osmium recommend the
use of nitric or nitro-muriatic acid to neutralize the potash ; sul-
phuric acid, to which Wollaston had recourse in his early ex-
periments, is now seldom em])loyed. Thomson, in his ' Che-
mistry of Inorganic Bodies,^ published many years ago, observes
that osmic acid has sometimes a tint of yellow.
It does not seem likely that the cork closing the neck of the
flask used for distillation had anything to do with the production
of osmious acid, if such took place ; the cork itself did not show
any appearance of being acted on, and there was no blackening
of its surface until some time after the experiment was ended.
The reduction of osmic acid generally rcsiilts in the formation
of the basic oxides ; Bcrzclius, however, observed that on adding
sulphurous acid to a solution of osmic acid, the latter passed
X2
296 Prof. J. Vr. Mallet on the Chemical and
through various shades of colour — yellow, orange-yellow, brown,
green, and at last blue ; he attributed these tints to the succes-
sive formation of sulphates of the binoxidc, sesquioxide^ and blue
oxide : but may not the first step in the reduction have been
osmious acid, giving the yellow colour ?
Another and altogether different view of the nature of the vola-
tile yellow substance above described was suggested as possible
by some remarks of Claus, in a recent paper " On the Tendency
to Reduction of Salts of Iridium " {Ann. der Chem. unci Pharm.
August 1858, p. 129). This author has shown that the platinum
metals fall naturally into three groups, in each of which are con-
tained two metals resembling in general habit and relations each
other more closely than members of the remaining groups. Pla-
tinum and palladium constitute the first of these pairs, iridium,
and rhodium the second, osmium and ruthenium the third. The
atomic weight of the first-m.entioned member of each pair is
higher than (nearly double) that of the second.
In the paper cjuoted, Claus remarks that the metal of lower
atomic weight in each of these groups is much more easily
reduced than the other from superior to inferior grades of com-
bination with chlorine : thus the bichloride of palladium is re-
duced with much greater ease to protochloride than is the corre-
sponding compound of platinum; and for the same reason, pro-
bably, the bichloride of rhodium is not known, but only the ses-
quichloride, while both salts of iridium can be easily obtained.
On this same principle Claus explains the fact that no oxide of
ruthenium homologous with osmic acid has been obtained, while
he gives the following reasons for suspecting the existence of
such an oxide : — " This opinion is based upon the fact, that in
my preparation of compounds of ruthenium, which can be ob-
tained only by energetic processes of oxidation, the material
worked upon, notwithstanding all my care and economy, gra-
dually diminished, and yet I have never succeeded in collecting
a volatile product. Once only, when I had fused ruthenium
perfectly free from osmium, with caustic potash and nitre, dis-
solved the mass in water, and decomposed it with nitric acid, I
observed a peculiar odour, quite distinct from that of osmic or
nitrous acid ; and afterwards, having covered the beaker, which
was smeared on the edge with tallow, with a plate of glass, I
remarked an unmistakeable blackening of the tallow, caused by
the reduction of a volatile metallic compound."
It seemed possible that the volatile yellow substance to which
the present paper refers might have been an acid oxide of ruthe-
nium*— RuO"^, RuO"*, or RuO' — and reducible with extreme
* If such a compound exist, an explanation may be found for the process
by which Fremy has obtained a lower oxide of ruthenium (probably the
Phtjsical Relations of Osmium. 297
facility, Claus and others liaving already noticed the reducing
effect of light upon salts of the platinum metals. A portion of
the crust of yellow acid from the sides of the tube was carefully
examined for ruthenium, the various tests given by Claus, as
M'cU as that recently proposed by Dr. Gibbs, being made use of;
but no proof of the presence of this metal could be obtained.
The properties of osmium and its compounds are very re-
markable, and render it a matter of no little interest to trace the
analogies of this rare substance and fix its place among the other
elements. It is described in most chemical works along with pla-
tinum and its associated metals, — mainly on the ground of com-
munity of origin ; for in many respects it is unlike the platinum,
palladium, rhodium, 8:c., with which it always occurs in nature.
All these metals arc commonly thought of as very infusible, of
great density, very slightly aft'ected by reagents, and very easily
reduced from their compounds to the metallic state ; when more
closely examined they are found to differ from each other in
many of their other properties. The arrangement by Claus of
the platinum metals in three groups, each containing one metal
of high and one of low atomic weight, viz.
Platinum, Iridium, Osmium,
Palladium, Rhodium, Ivuthenium,
has been alluded to above ; the two members of each group are
more closely related to each other than to any of the rest.
Osmium and ruthenium are clearly the most electro-negative of
the series. Graham has inferred the isomorphism of platinum,
palladium, iridium, and osmium, from the fact that their potassio-
chlorides all crystallize in the form of the regular octahedron :
the corresponding compound of ruthenium has since been added
to the list, while that of rhodium is still unknown. The occur-
rence of two salts under the same form, in the regular system, of
course does not of itself sufliee to establish the relation of iso-
morphism between them ; iridio-chloride of potassium seems how-
biuoxide) in crystals. He roasts tlic jiowder of i)latinnm-rcsiiluc in a stream
of air drawn through a porcchiin tube at a brij^ht red heat ; osmic acid volati-
lizes, and is said to carry with it mcchanicdlhj the oxide of ruthenium,
which deposits upon fragments of porcelain placed in the cooler j)art of the
tube. But the oxide is in distinct crystals, and can therefore scarcely be
conceived of as a powder borne alonp in a merely mechanical way by a
stream of vapour ; and, moreover, there is no reason for oxide of ruthenium
only being so borne along, while other substances of no greater density re-
main behind. Is it not more likely that a volatile and very easily reducible
homologue of osmic acid is formed, and almost immediately afterwards
decom])osed, depositing the binoxidc of ruthenium?
298 Prof. J. W. Mallet on the Chemical and
ever to be capable of crystallizing in all proportions with the
platino- and osmio-chlorides.
The interesting fact has been discovered by Glaus, that osmio-
cyauide and ruthenio-cyanide of potassium are strictly isomor-
phous with the well-known ferrocyanide, crystalUzing with it in
all proportions, and even giving very similar precipitates with
various metallic solutions ; so that, in these double cyanides, os-
mium and ruthenium are capable of taking the place of iron.
In the greater number of its relations, however, osmium pre-
sents itself as a member of the arsenic group of elements. This
has been noticed by some recent authors, as by Prof. Dana iu
the arrangement of the elements adopted in his ' System of Mi-
neralogy,^ and by Prof. ^Miller, who says in his lately published
' Elements of Chemistry,^ that " it presents more analogy with
arsenic and antimony than with the noble metals. ^^ Fremy, too,
compares osmium in platinum ore to arsenic iu the native arse-
niurets.
Nitrogen, phosphorus, arsenic, antimony, and bismuth are
generally recognized as forming a distinct and natural group of
elements ; and into this group it seems from many considerations
that osmium, and probably ruthenium, ought to be introduced.
They have some analogies with other natural families, just as
arsenic is allied to sulphur in native sulph-arseniurets, and nitro-
gen and chlorine exhibit some resemblance in the nitrates and
chlorates; but here appear to be their closest relations. It may
be interesting to notice some of the principal points of resem-
blance to or difference from tliis group.
Iridosmine occurs in crystals closely related in form to those
of arsenic, antimony, and bismuth in the metallic state. The
analyses of iridosmine are not yet sufficiently numerous or ac-
curate to enable us to decide upon its normal composition ; but
it seems probable that the two metals occur in variable propor-
tions, and are in this mineral isomorphous, thus establishing, as
noticed by Dana, a connexion between the arsenic group and
that of the distinctly basic metals, as the arsenic and sulphur
groups are united through homoeomorphous bismuth, tetrady-
mitc and tellurium. Dana places iridium in the same section
with iron, among the metals whose most stable grades of oxida-
dation are the protoxide and sesquioxidc ; but the statement of
Glaus, that the hinoxide of iridium is the most stable and easily
prepared compound with oxygen, would remove this metal, as
also perhaps platinum and palladium, from the iron section to
that containing tin and titanium; and the propriety of this
transfer may be supported by the relationship of Fremy^s cry-
stallized oxide of ruthenium (doubtless the hinoxide) examined
by Senarmont : this was found to be homcEomorphous with
Physical Relations of Osmium. 299
stannic and (the rutile form of) titanic acid. The bichloride of
tin and potassium^ too, is reported as crystallizing in regular
octahedrons, like the corresponding salts of iridium, platinum,
and ))alladium.
The arsenic section, as given by Dana, includes nitrogen,
phosphorus, arsenic, antimony, bismuth, osmium, and tellurium.
The last-named is marked as doubtful, and should decidedly be
])laced with sulphur and selenium, to which it is analogous in
by far the greater number of its compounds.
In one of the interesting memoirs lately published by Dumas,
on the numerical relations subsisting among the atomic weights
of the elements, the arsenic series is thus given : —
Atomic weights.
Nitrogen .... 14
Phosphorus . . . . 14 + 17 = 31
Arsenic 14 + 17 + 44=75
Antimony .... 14 + 17 + 88 = 119
Bismuth 14+17 + 176 = 207
and the parallelism of this series with that of chlorine, iodine,
&c., is supposed to be shown in the follo\A'ing lines : —
F (19) CI (35-5) Br (80) I (127)
N (14) P (31) As (75) Sb (122)
in which a common difference of 5 is assumed between the two
members in each of the vertical columns (a difference not strictly
brought out in the case of phosphorus and chlorine), and in
which a higher atomic weight is assigned to antimony than in
the preceding Table. Osmium is not included ; but in a supple-
mental note since published, we find it placed, with an equivalent
somewhat higher than that usually adopted, in the sulphur group,
serving to complete the following two lines of equivalents : —
Mg (12-25) Ca (20) Sr (4375) Ba (68-5) Pb (103-5)
0 (8) S (16) Se (39-75) Te (64-5) Os (99-5)
between the paired members of which a common difference of 4
is supposed to exist.
Let osmium and ruthenium be brought into the arsenic group,
and the series of atomic weights will then stand thus : —
Atomic weights.
Nitrogen . . . . 14
Phosphorus . . . 14 + ] 7 = 31
Ruthenium . . . 14 + 17 + 22 = 53
Arsenic .... 14 + 17 + 44=75
Osmium .... 14+17 + 66 = 97
Antmiony .... 14 + 17 + 88=119
Bismuth .... 14+17 + 176 = 207
300 Prof. J. W. Mallet on the Chemical and
The atomic weights of ruthenium and osmium are here assumed
as 53 and 97 ; numbers not differing more widely from those
commonly received — 52*2 (Claus) and 99"6 (Berzelius) — than
do several of those assumed by Dumas. Our knowledge of these
two equivalents is based upon very limited data, and can but be
looked on as merely approximative. As regards osmium, Fremy
says that in several cx])eriments he has obtained an equivalent
number lower than that given by Berzelius ; and the vapour-
density of osmic acid, which we shall notice presently, points to
an equivalent close to 97. A redetermination of this equivalent
is very much to be desired.
Taking the series as given above, we find ruthenium and
osmium to fall in between phosphorus and arsenic, arsenic and
antimony, — the numbers from phosphorus to antimony inci'cas-
ing by 22 — 41 — 6G — 88, just as in the following group given
by Dumas : —
Atomic weights.
Chromium .... 26
Molybdenum. . . . 26 + 22 = 48
Vanadium . . . . 26 + 44 = 70
Tungsten 26 + 66 = 92
and we may arrange the two series in parallel lines,
P (31) Ru (53) As (75) Os (97)
Cr (26) Mo (48) V (70) W (92)
These numerical relations are of very little importance in
themselves, v»'hen we employ the small numbers of the hydrogen
scale of equivalents, and especially when we permit ourselves to
alter the numbers themselves to any extent, however small ; but
they acquire more interest when they present us with groupings
of elements which we acknowledge on other grounds to be natu-
rally related. In such cases, when the homology is distinctly
marked, we may even be justified in taking some liberties for
the moment with the numbers standing, often with but slender
evidence to sup])ort them, for the equivalents of the less known
elements ; and we may, perhaps, thus be directed to errors of
determination which future experiments will clear away.
The bodies named in each of the two lines just given are
homologous in many respects besides that of atomic weight, and
a connexion between the two series, through vanadium, has
lately been shown by Schafarik. There is a clear resemblance
running through the formula and properties of their oxides. In
the chromium series — a very natural one — the most important
oxides are the metallic acids of the composition MO^; we have
also in each case a binoxide, MO'^ ; but the sesquioxide is pro-
Physical Relations of Osmium. 301
mincnt only in the case of chromium itself, and indicates the
relation of this metal with iron.
In the arsenic series the known oxides are the following : —
NO PO RuO AsO(?)
OsO SbO (?)
BiO (?)
Ru^ 03 (?)
Os2 03(?)
N02 RuO^
Os02
N03 PO^^ RuO=^ As03
Os03 Sb03
BiO'^
NO^ P04 (?)
OsO'* SbO^
BiO^
NO^ PO^ AsO^
OsO^ SbO^
BiO^ (?)
The prominent compounds in the Table are the acids MO^ and
MO^ ; with respect to the separate columns^ the following facts
arc noticeable.
The oxides of nitrogen are well known ; the regularity obser-
vable in this column causes it to be frecpicntly used as an
illustration of the/' lav/ of multiples/^ NO and NO^ are usually
said to be neutral ; but the latter plays the part of a base in con-
tact with sulphuric acid^ as in the crystals of the oil of vitriol
chambers, and possibly the former may do so, too, in the nitro-
sulphates (KO, NO, SO^ and NII^O, NO, SO^?) obtained by
Davy by bringing nitric oxide in contact with an alkaline sul-
phite. NO^ and NO'^ are well-known acids. It is doubtful
whether hyponitric acid (NO'*) is capable of combining with
bases and forming salts ; in contact wath the alkalies it yields a
mixture of nitrites and nitrates, yet, ivhen out of contact of bases,
it seems to be a body of more stability than either NO^ or NO^ [an-
hydrous] .
In the column of the oxides of phosphorus, we have first the
very anomalous suboxide (P'"0), which is probably the only
marked exception to the homology running through the whole
table. Before the discovery of red (amorphous) phosphorus by
Schrotter, this substance was, no doubt, to some extent con-
founded with phosphoric oxide, and may even now throw some
doubt upon the cases in w Inch the latter seems to have been ob-
tained pure and to have yielded a formula supported by trust-
worthy analyses. PO, unlike the other protoxides of tlie series,
is usually considered an acid ; but as it has not been obtained in
the separate state, and all the hypoj)hosphites contain water, it
may be reasonably assumed that the formula of the acid should
include hydrogen. PO' is doubtful : this may, perhaps, be the
composition of Pelleticr's phosphorous acid, produced by the
slow combustion of phosphorus, a body which undergoes no
further oxidation by {)rolonged exposure to the air, and which,
in contact with bases, yields mixed phosphites and phosphates.
The last term in the column, phosphoric acid, is well known.
302 Prof. J. ^Y. :Mallet on the Chemical and
The existence of a distinct protoxide of arsenic^ a.? of antimony
and bismuth, is doubtful. Arsenious acid is n feeble, volatile, me-
tallic acid — feebler in its relations as an acid than arsenic acid,
and volatilizing at a lower temperature than the latter. Arse-
nious acid, moreover, volatilizes at a temperature below that
reqviired by metallic arsenic.
In the antimony column, the oxide SbO^ is usually viewed as
a weak base, but seems also to be capable of uniting as a feeble
acid to the alkalies, and even of expelling carbonic acid from
their carbonates (Liebig). The isodimorphism of SbO^ and
AsO^ is well established. SbO'*^ is volatile at quite a moderate
temperature, while metallic antimony requires at least a white
heat to vaporize it. SbO^ is a body of distinctly acid properties.
BotJi SbO'^ and '&\>0^ are converted bij heating in the air into SbO*
— the so-called antimonious acid, which seems therefore to be
the most stable oxide when strong bases and acids are not pre-
sent. It is most probable that, as Fremy maintains, SbO^ is not
itself an acid, but that a so-called alkaline antimonite is, in fact,
a mere mixture of an antimoniate with the compound of anti-
monic oxide and alkali (2SbO-^ = Sb03-f-Sb05).
In the bismuth column, the teroxide is homologous as a base
with teroxide of antimony, but shows little tendency to play the
part of an acid with even the strongest bases. This oxide and
the metal itself are volatile at high temperatures. BiO'* also
seems to be devoid of acid properties ; but the compound BiO^
probably exists, and is homologous with SbO'^, forming alkaline
salts of little stability.
Comparing now ruthenium and osmium with the above recog-
nized members of the arsenic group, we find, first, that both
metals form protoxides, which are feeble bases, as are probably
the corresponding compounds of the other members of the group.
We next meet with the sesquioxides, whose formula is excep-
tional in the series ; but for neither metal has this grade of oxi-
dation been obtained in the free state and pure, and in the case
of osmium its existence may be gravely doubted. Anhydrous
Ru^ 0^ is supposed by Claus to be formed during the roasting of
metallic ruthenium in the air at a high temperature ; but only on
the ground that the absorption of oxygen slackens when about
enough has been taken up to form this compound, and that the
proportion necessary for the binoxide is never fully attained.
Claus, however, describes a sesquichloride wixh which double
salts are formed by the chlorides of potassium and ammonium,
and we must therefore assume a sesquioxide also. Sesquioxide
of osmium is quite unknown in the separate state ; and the belief
in its existence is founded solely upon the preparation by Ber-
zelius of a dark brown substance, supposed to consist of the
Physical Relations of Osmium i 305
sesquioxide united to amuionia, which, dissolved in hydrochloric
acid, yields a brown compound, supposed to be the sesqui-
chloride of osmium and ammonium. Neither of these, however,
can be crystallized, nor has the constitution assigned to either
been supported by an analysis. The so-called ammonio- sesqui-
oxide detonates when heated (sometimes with much violence, as
I have noticed in removing by heat the deposit of this substance
which forms on the end of a retort-neck during the distillation
of osmic acid into a receiver containing ammonia), and hence is
probably analogous to fulminating platinum, containing perhaps
the binoxide of osmium. The binoxide itself is a feeble base,
the characteristic colour of whose salts in solution is yellow, as is
the case with the corresponding compounds of iridium. Similar
remarks apply to the binoxide of ruthenium — probably the body
obtained, as we have shown, by Fremy in crystals. The teroxide
of osmium is the body supposed to have been isolated in the ex-
periment described at the beginning of this paper. Its position
as a feeble acid, capable, however, under some circumstances, of
playing the part of a base, its fusibility and volatility (greater
apparently than those of osmic acid, as nitrous acid is more
fusible and volatile than hyponitric), its probable crystallization
in octahedrons of the regular system, in which arsenious acid
and teroxide of antimony are also found, all tend to indicate
homology with the other teroxides of the arsenic group. The
general relations of rutheuic acid, so far as these are known,
place it in a similar position. Just as we find hyponitric acid
(NO^) and antimouious acid (SbC*) to be the most stable of the
higher oxides of nitrogen and antimony, so the well-known osmic
acid (OsO'*) seems to be the grade of oxidation which osmium
most readily assumes and retains when not in contact with bases.
OsO^ and OsO^ (the latter as described by Fremy) seem scarcely
capable of existing in the separate state ; when set free from their
salts they soon pass into OsO'* ; while it may as well be doubted
that the latter ever exists as a distinct acid in combination with
bases, as that NO'* or SbO"* does so. No so-called osmiate has
ever been analysed; the saturating capacity of the acid, if it be
such, is unknown ; wlicn free and in solution in water, it has no
acid reaction ; it does not displace carbonic acid from the carbo-
nates, and it is itself expelled by heat from most of its supposed
compounds, and is separated in ])art by water even from potash
and soda. No compound of OsO' with a base has been obtained
in crystals, while Fremy states that he has crystallized the alka-
line salts of both OsO^ and OsO^. KuO"' and KuO^ are as yet
unknown.
The tendency throughout the whole arsenic group is mani-
festly to the production of the acid compounds MO^ and MO^j
304 Prof. J. W. Mallet 07i the Chemical and
the former the more fusible and volatile body, the latter the
stronger acid. In addition, we have some cases of the prot-
oxide (MO), a feeble base, and the binoxide (MO^), a body of
still more feebly basic properties, verging upon the acids. All
other grades of oxidation, so far as they exist at all, may per-
haps be correctly viewed as compounds of the preceding m/er 5e.
The stability of the oxide (MO'*) in the separate state is remark-
able ; its formula is one of rare occurrence.
The affinity of all the elements of the group for oxygen is
considerable ; it is so even in the case of osmium and ruthenium,
usually placed among the noble metals. Dumas {Traitede Chim.
app.) states that osmium does not oxidize at common tempera-
tures, nor even at 100° C. ; but I have obtained conclusive evi-
dence that oxidation may go on slowly even at the ordinary
atmospheric temperature. The paper label and the cork of a
tube containing pure metallic osmium have in the course of se-
veral years become blackened, precisely as organic matter is by
the fumes of osmic acid, the black tint on the paper decreasing
from the mouth of the tube along the outside. A piece of white
paper, in which some black platinum residue had been wrapped,
was strongly stained in the immediate neighbourhood of the pow-
der in the course of a few weeks. The same effect is distinctly ob-
servable even upon the paper label placed inside a tube of native
iridosmine (Siberian) in the usual coarse grains — a specimen which
has lain among other minerals, and has never been placed near
any artificial preparations of osmium. Osmium, like arsenic and
antimony, is clearly capable of slowly taking up oxygen at com-
mon temperatures. At a red heat, roasting in a current of air
affords, as is known, a good method of obtaining osmic acid from
the iridosmine of platinum residues — just as by similar roasting
arsenious acid is prepared from the native arseniurets.
It would be a matter of much interest to compare osmium with
its supposed homologues under circumstances in which we should
expect it to play an electro-negative part. Fremy has announced
his belief in the existence of an osmiuretted hydrogen ; but such a
body has not yet been isolated and described. Compounds of
the metal with ethyle, methyle, &c., would be w^ell worth exami-
nation ; and it is not unlikely that such might be prepared from
a body which in some states of combination exhibits such a high
degree of volatility.
The earlier experiments of Deville and Debray upon the pla-
tinum metals seemed to have shown that both osmium and ru-
thenium could be volatilized, at exceedingly high temperatures,
without previous fusion ; if this were contirmed, a strong point
of resemblance with arsenic would be made out ; but it appears
from a more recent paper, that osmium at least may be fused and
Physical Relations of Osmium, 305
obtained as a perfectly compact mass, the apparent volatility of
the metal being due doubtless to previous oxidation, the cru-
cibles used being permeable to air. We have seen, as regards
arsenic and antimony, that their oxides are more volatile than the
metals themselves.
It was lately stated that osmium may be obtained in crystals by
the same means as those used for boron and silicon, but I have
as yet seen no account of the form which it assumes.
Deville has furnished another interesting fact with respect to
osmium, by determining the density of the vapour of osmic acid
which he has found = 8*88. This, if we take the generally
received atomic weight for osmium, gives tlie atomic volume
1 m 'C
^v-7j7r = l i'82, indicating a condensation to 2 vols. If we now
O'oo
calculate back to the theoretical atomic weight, we get (14-57'
X 8-88) — 32 = 97'38, a number closely approaching 97, which
as we have seen, brings the equivalent of osmium into simple
and harmonious relation with those of the other elements of the
arsenic group.
The specific gravity of fused metallic osmium having been
lately determined by Deville = 21 "4, there can be little doubt
that all the metals of the platinum family possess the same atomic
volume when in the free state, about 4Gor4'7: the specific
gravity of ruthenium is not yet known with accuracy, but such
experiments as have been made render it improbable that it will
prove an exception. This number is about one-fourth the mean
of the atomic volumes of the long-recognized members of the
arsenic group ; but these latter differ so widely among them-
selves*, that the comparison is of little or no value. It Avould
be desirable to get a good determination of the density of osmic
acid in the solid state, so that its atomic, volume might be calcu-
lated and compared with that of antimonious acid.
The specific heat of osmium, so far as its value as a physical
character goes, opposes the introduction of this element into the
arsenic group. It has been determined by Regnault =-03063 •
multiplying now by the equivalent 97, we have the product
2*9711, thus placing osmium in the list of the elements (inclu-
ding the majority), for which the product of specific heat by
* I'l'^^Pl'O"'^ r83 (Schrottcr) =^^'^'^'
Arsenic rT= m .i ^ =^^"23.
5'()/ (Ilerapath)
Antimony — ^ ._, =17-7G.
6/ (Karsten)
Bismuth 207 (Marchand —opio^
ys &Schccrer)
306 Royal Society : —
atomic \A'eight is nearly 3j while for phosphorus, arsenic, anti-
mony, and bismuth, the product thus obtained is twice as great,
or about 6. In this respect, however, osmium probably resem-
bles nitrogen — the latter examined, as it necessarily is, in the
gaseous form.
It is to be hoped that the conducting power for heat and elec-
tricity of compact osmium will soon be examined; nothing is as
yet known of these characters.
Lastly, as regards the magnetic relations of the element : it is
placed, with some doubt, by Faraday in the paramagnetic class ;
the metal and its protoxide were found to act feebly in this
sense, while pure osmic acid is said to have shown itself clearly
diamaynetic. The strongly diamagnetic character of phospho-
rus, antimony, and bismuth would render a re-examination of
this point interesting. Arsenic, however, is said to be very
feebly diamagnetic, and is placed by Faraday close to osmium
in the list of metals examined, though on the opposite side of the
line of magnetic neutrality or indifference.
Reviewing, now, the united physical and chemical characters
of osmium, and comparing them with those of the generally re-
cognized members of the " arsenic group,'^ we are, I think, jus-
tified in concluding that here this curious metal should be placed
in a natural arrangement of the elements ; while important di-
stinctions seem to separate it from some, at least, of the platinum
metals, with which it is usually associated and described.
XLI. Proceedings of Leattied Societies.
ROYAL SOCIETY.
[Continued from p. 235.]
Nov. 17, 1859. — Sir Benjamin C, Brodie, Bait., Pres., in the Chair.
THE following communications were read : —
" Researches on the Phosphorus-Bases." — No. YI. Phospham-
monium-Compounds. By A. W. Hofmann, LL.D., F.R.S. &c.
In several previous communications I have shown that dibroniide
of ethylene is capable of fixing either one or two molecules of tri-
ethylphosphiue, a monatomic and a diatomic bromide being formed,
which I have respectively represented by the formulae —
^Monatomic bromide, r C H.
C,, H,, PBr,= (C, HJ" Br,+ (C, U,), P=
L(C,II,Br)
and
C4 H- , p
C,H, 1^
Br
C.« H3, P, Br = (C, IIJ" Br, -I- 2 ((C, H,)3 P) =
Diatomic bromide
.(C.HJ"J J
Br,
Dr. Hofmann on Phosphammonium Compounds. 307
Ther are other products formed, resulting from secondary reac-
tions.
It was not quite easy to obtain a sufficiently satisfactory experi-
mental foundation for the diatomic nature of the second compound.
This substance presents an extraordinary degree of stability ; in its
general characters it is closely allied to the numerous monatomic
bromides, both of the nitrogen- and of the phosphorus-series, which
in the course of these researches have come under mv consideration.
Lastly, the oxygenated derivative of the bromide resembles so per-
fectly the monammonium- and the monophosphonium-bases, that
more than once during my experiments I was inclined to doubt the
correctness of my interpretation.
There is no direct proof of the diatomic character of the com-
pound. Why should we reject the simple formula deducible from
experiment ? The hydrocarbons €„ H„ are very prone to molecular
transformations without change of composition. The idea suggested
itself, that the diatomic saline molecule might be split into two
monatomic saline molecules,
[(C, H3), (C, HJ" PJ" Br, = 2([(C,H J3 (CJiy P] Br).
It is true C, H^ figures in this formula as monatomic, whilst we
should expect it endowed with diatomic substitution-power. But
the connexion between composition and substitution-power is by no
means finally settled ; in fact, we know of many cases in which,
xmder conditions not sufficiently established, the atomicity of a mole-
cule changes : witness the radical " allyle," which is capable of re-
j)lacing one or three equivalents of hydrogen.
But without going this length, the scission of diatomic ethylene
into two monatomic molecules may take place in many other ways.
The transformation of dibromide of ethylene into hydrobromic acid
and bromide of vinyle,
(C,H,)"Br,=HBr-f(C,H3)Br,
is a familiar example. The sjilitting of the ethylene-compound into
bromide of formyle and bromide of methyle,
(C. HJ" Bt^= (C, H) Br-f- (C, H3) Br,
has never been observed, but did not appear altogether unlikely.
Our analytical methods are insufficient to distinguish between
[(C, H,)3 (C, H,) P] Br and [(C, U^, (C, H) P]Br ;
and what I have represented as a diatomic ethylene-compound
might have been, after all, a monatomic bromide — the bromide of
formyl-triethylphosphonium, the complementary methvle-compound
[(C.II,),,(C,H3)P]Br
existing possibly among the secondary products of decomposition.
In the presence of these and several similar self-raised objections,
by which every observer endeavours to test the truth of his con-
clusions, I was induced again to appeal to experiment.
The prosecution of this line of the inquiry has led me to the disco-
very of a new class of diatomic bodies, which, while it confirms incou-
testably the correctness of my interpretation, appears to claim the
attention of chemists for several other reasons.
308
Royal Society : —
I have established, in the first place, that the monatomic bromide
[(C,H,)3(C,H,Br)P]Br
may be readily converted into the diatomic bromide
__[(C,_H,),(CJI,)"Pj"Br3
by the simple addition ot triethylphosphine. Nothing is easier than
to prove the transformation, the j)latinum-salt of the two bases pre-
senting a remarkable difference of solubility, and other differences
not less striking.
To remove every doubt, the bromide, obtained by treatment of the
brominated bromide with triethylphosphine, was converted into the
corresponding iodide, which in its properties and composition -was
found to be identical in every respect with the characteristic iodide,
which I have fully described in my last note ixpon this subject.
The transformation of the monatomic into what I have represented
as the diatomic compound being satisfactorily established, the con-
clusive experimental demonstration of the diatomic nature of the
latter presented itself without difficulty in the conception of bromides
containing at once phosphorus and nitrogen, the molecular expression
of which would no longer admit of division.
This class of dibromides actually exists ; they are readily produced
by submitting the bromide of the brominated body to the action of
ammonia or monamines instead of triethylphosphine.
I have formed as yet only three representatives of this new class of
bodies, which 1 propose to designate as phosphammonium-com-
pounds ; their examination is sufficient to fix the character of the
class ; it would have been easy to construct scores of similar bodies.
Action of Ammonia upon the bromide of the brominated body.
The two substances, especially when in alcoholic solution, luiite
with evolution of heat —
"(C,H,)3}p""
[(C,H,)3(C,H,Br)P]Br-fH3N=
(C,HJ"
N
Br.
Both the bromide and the corresponding chloride are very soluble,
and little adapted for analysis ; I have therefore fixed the uature of
this body bv the preparation and analysis of the platinum-compound.
For this purpose the bromide generated in the above reaction was
treated with oxide of silver ; it is thus converted into a powerfully
alkaline solution obviously of the dioxide,
1" "
(C.H,)3
(C,H,)"
N
>o,.
which, saturated with hydrochloric acid and mixed with dichloride of
platinum, furnished a fight-yellow crystalline platinum-salt, recry-
Btallizable from boiling-water, and containing
[(C, H,)3 H3 (C, HJ" PN]" Cl„ 2PtC]3.
On the Behaviour of the Aldehydes with Acids.
309
Action of Ethylamine and Trimethylamine upon the bromide of the
hrominated body.
The phenomena observed with ethylamine and trimethylamine
are perfectly analogous. These substances furnish, with the hromi-
nated bromide, new and very soluble dibromides, containing re-
spectively
(C.H,)3
(C,H3)H,
P
N
Br, and
H,V'
(C,H,)' ,
.(C,H3)3 N
Br„
which, by treatment with oxide of silver, are converted into the cor-
respondhig powerfully alkaline oxides
(C,H,)3
_(CJI,)H3[n_
Ho
O,
and
(C,H,)3
(C.HJ'j
(C.H3),
P
N
H,
O,
and yield, by saturation with hydrochloric acid and precipitation with
dichloride of platinum, two splendid platinum-salts crystallizing in
long golden-yellow needles, and containing respectively
[(C, 11,)^ (C, HJ" 11.. PN]" CI, 2Pt Cl„ and-
[(C, H3)3 (C, H3)3 (C, II,)" PN] " CI, 2Pt CI,.
By the formation of the phosphammonium-compounds, the nature
both of the diammonium- and of the diphosphonium-series appears
to me finally established.
It will be interesting to ascertain whether the brominatcd bromide,
when submitted to the action of mouarsines and monostibines, will
give rise to the formation of phospharsonium- and phosj)ho-stibo-
nium-bases. The solution of this cpiestion will not be difticult.
" On the Behaviour of the Aldehydes with Acids." By A. Geuther,
Esq., and R. Cartmell, Esq.
The authors of this pai)er, with a view of obtaining a series of
combinations homologous with those already obtained from glvcol by
<^'"' 1
"Wurtz — viz. diacetate of glycol, Cj H3 O, >■ O,, and the isomeric body
c.H3o:j .
of Geuther from common aldehyde, by the action of anhydrous
acetic acid, — have subjected common aldehyde, acroleine, and oil of
bitter almonds to the action of hydrochloric, hydriodic, and sul-
phurous acids.
I. Acroleine, — Metacroleine.
1. Acroleine and Hydrochloric Acid.
By acting on acroleine, C,; 11, O^, with dry hydrochloric acid gas,
a body is formed of the composition C,, 11, O. CI, resulting from a
direct combination of one atom of aldehyde with one atom of the
acid. This substance is insoluble in water, and can be waslud with
it in order to free it from any excess of acid or acroleine which may
be still present. By drying, which can only be done over sulphuric
acid at low temperatures, the bodv, for which the authors ])ropose
Phil. Mag, S. 4. Vol. 19. No.' 137. April 18G0. Y
310 Royal Society : —
the name of hydrochlorate of acroleine, is obtained in a mass of
white crystals, presenting a texture hke that of velvet. It melts at
32° C. into a thick oil, having a smell of slightly rancid fat. It is
readily soluble in alcohol or ether, on evaporation of which it re-
mains behind as a thick oil. When boiled with water, it remains, as
far as can be seen, unchanged. Dilute solutions of the alkalies ap-
pear not to act on it. Heated with solution of ammonia in a sealed
tube at 100° C, it is decomposed, chloride of ammonium and acroleine
ammonia being the result. It does not combine with bichloride of
platinum when in solution in alcohol, and very slowly reduces boiling
ammoniacal solution of nitrate of silver. Heated alone, it decom-
poses into acroleine and hydrochloric acid. By the action of concen-
trated hydrochloric acid acroleine is set free. Dilute sulphuric and
nitric acids decompose it likewise, setting acroleine free. Heated
with hydrate of potash it gives off hydrogen ; and there distils at
the same time an oily body, which solidifies into magnificent colour-
less crystals, analyses of which prove it to be an isomeric acroleine,
for which the authors propose the name Metacroleine.
Metacroleine as thus obtained is insoluble in water, but is capable of
being recrystallized from alcohol or ether. The crystals form very
long needles, more especially when melted metacroleine before solidi-
fying is allowed to flow about in a glass tube. They resemble
very much in appearance crystals of acetamide, possess a peculiar
aromatic smell, and have a taste at first producing a cooling and
afterwards a burning sensation. They are lighter than water. They
melt at about 50° C, becoming solid at about 45°C, Before melting
they are somewhat volatilizable, on which account they can be
distilled in the vapour of water. On being heated, metacroleine is
changed into common acroleine. Dilute alkalies do not effect any
change in this substance. By heating with mineral acids, common
acroleine is set free. On leading dry hydrochloric acid gas over
metacroleine in a bulb-tube, the metacroleine melts and combines with
the acid, producing the already-named hydrochlorate of acroleine.
From this behaviour, the authors believe the acroleine contained in the
compound of h^^drochloric acid to be metacroleine, and not common
acroleine. If metacroleine be viewed as Cj^ H^ O^, the formula of the
hydrochloric acid compound would then be Cj^ H^ O^, 2HC1; and
the formation of metacroleine mav be assumed to take place accord-
ing to the following equation, C.^H.O,, 2HCl-f2KOHO=C,,H,0,
-f 2KCl-f 4H0. The evolution of hydrogen has been found to be
the result of a secondary action.
2. Acroleine and Hydriodic Acid.
These substances act very violently on each other if the acid in
the gaseous form be led into acroleine, producing a hissing noise, as
when red-hot iron is plunged into water. The resulting substance is
insoluble in alcohol, ether, acids, and alkalies. Bisulphide of carbon
dissolves out a little free iodine. Heated alone, iodine is set free.
3. Acroleine and Water.
Acroleine mixed with two or three times its volume of water, and
exposed to the temperature of boiling water for eight days, under-
On the Behaviour of the Aldehydes with Acids, 311
goes a gradual change. Acrylic acid is produced, and a resinous
substance, soluble in ether, melting at about 60°, and becoming
solid at 55°C. At common temperatures it is hard and brittle, like
resin. The per-centage composition of this resin, on analysis, was
found to be the same as that obtained by Redtenbacher, and named
Disacrylic resin*, viz, carbon G6'6, hydrogen 7'4.
4. Metacroleine and Hydriodic Acid.
"When dry hydriodic acid gas is passed over dry metacroleine, the
latter melts, and changes into a heavy yellow solution, resembling in
smell and appearance the hydrochlorate of acroleine. It caii be
washed with water, and appears at ordinary temperatures to solidify
into crystals ; placed over sulphuric acid to dry, it decomposes, be-
coming brown, and setting iodine free. From the analogy in its
formation, this compound can be properly viewed as hydriodate of
acroleine.
II. Aldehyde.
1 . Aldehyde and Hydrochloric Acid.
Lieben found that by the action of hydrochloric acid on aldehyde,
a body of the composition C^ H^ O^ CU was produced, having a con-
stant boiling-point of from 116° to 117° Cf
The authors confirm Lichen's statement as to the replacement of O^
by CI2 in two atoms of aldehyde, and have further obtained a new
combination, analysis of it giving the formula as Cj.^ H,^ O^ CL, in
which two equivalents of oxygen are replaced by the same number of
equivalents of chlorine in three atoms of aldehyde. By the action of
water, this compound, like that of Lieben, is resolved into hydro-
chloric acid and aldehyde. By heat, it is broken up into aldehyde
and the body C^ H^ O^ Cl^. The authors propose for it the name
protoxychloride of aldehyde.
2. Aldehyde and Hydriodic Acid.
By the action of hydriodic acid on aldehyde a compound is pro-
duced that decomposes with water into the aldehyde and the acid
again, on which account it could not be purified. On heating, it is
suddenly decomposed at 70° C, leaving a black resinous residue,
which on distillation gave off vapours of iodine. In its mode of
formation it is analogous to the bodies produced by the action of
hydrochloric acid on aldehyde.
3. Aldehyde and Sulphurous Acid — Elaldehyde.
Dry sulphurous acid gas led into anhydrous aldehyde in cold water
is absorbed with great avidity, 1 1 grannnes of aldehyde absorbing 19
grammes of the acid, whilst an increase of volume takes place. The
absorption-coefficient of aldehyde for this acid was found to be T-l
times greater than that of alcohol for the same, and seven times greater
than that of water for it. No chemical combination appears to take
place, as, on passing a stream of carbonic acid through the fluid at a
slightly elevated temperature, almost all the sulphurous acid can be
driven out again. If aldehyde, saturated with sulphurous acid, be
left for about a week at ordinary temperatures in a well-stoppered
* Chem. Gaz. vol. i. p. 744. + IbiJ* ^ol- xvi. p. 215.
Y2
313 Hoyal Society .—
bottle, it suffers in this time almost a complete change into a body
for which the authors propose at present the name Elaldehyde.
To obtain it pure, the fluid is mixed uith as much water as is neces-
sary to dissolve it up ; the acid is saturated by degrees with chalk,
and the fluid obtained is distilled so long as oily drops pass into the
receiver. The common aldehyde is separated in a resinous form by
digesting for some time with solution of caustic soda or potash. By
repeated distillation, the elaldehyde can be obtained free from every-
thing but a little water. Analysis gives the formula of this aldehyde
as C^ H^ O.,. It is therefore isomeric with common aldehyde. As
it was obtained in quantity by the foregoing method, its properties
were further examined. Its boiling-point was found to be 124° C,
and solidifying-point 10° C. Whilst solidifying it likewise starts
into crystals, the melting-point of which is also 10° C. The alde-
hvde here described under the name Elaldehyde is identical with
that of Weidenbush*. Its mode of production from common alde-
hyde is the same ; its boiling-point likewise agrees with that of
the aldehyde of Weidenbush.
The elaldehyde of Fehling the authors believe to be identical
■with that they have obtained, and also that obtained by Weidenbush.
That which goes far to prove the identity of the two latter is their
vapour-densities. That of Weidenbush's is given as 4"58, whilst that
of Fehling's is 4-52; both are converted into common aldehyde by
heating gently with dilute sulphuric acid, and both crystallize at low
temperatures. The only material discrepancy between them is the
boiling-point of 94° C. given by Fehhng for elaldehyde, whilst Wei-
denbush gives the boiling-point of his aldehyde as 125° C.
III. on of Bitter Almonds.
1. Oil of Bitter Almonds and Hydrochloric Acid.
This acid does not combine with oil of bitter almonds. Ex-
periments made in sealed tubes, heated first to 100° C, and after-
wards to 200°, gave no signs of a combination having been effected.
2. Oil of Bitter Almonds and Hydriodic Acid.
Much better results can be obtained when hydriodic acid is
allowed to act on oil of bitter almonds. The gas is absorbed, pro-
ducing an increase of volume and of temperature, and at the same
time a little water. At the end of the operation two layers appear,
of a dark-brown colour. The upper one, which is about a sixth
part of the quantity of the under one, consists of concentrated hy-
driodic acid, whilst the under one, a heavy oil, is a compound of
iodine and oil of bitter almonds. To obtain the substance in a pure
state, it was first washed well with water to remove excess of the
acid ; next treated with moderately strong solution of sulphite of
soda, to remove any excess of oil ; lastly, on washing with water, the
salt was removed from it. It can be dried rapidly over sulphuric
acid at a temperature not higher than 20° C. A higher temperature
produces gradual decomposition. In the preparation of this sub-
stance, G grammes of oil of bitter almonds absorbed 1 1 grammes of
hydriodic acid gas. Analyses of the substance lead to the formula
* Chem. Gaz, vol. vii. p. 34.
On the Behaviour of the Aldehydes with Acids. 313
C^^ni^O, I,, which will be observed to be 3 atoms of oil of bitter
almonds, in which 2(0.J is replaced by 2(1,). The authors pro-
pose for it the name Oxyiodide of Benzaldehyde= The substance
tlius obtained molts at 2S° C, and solidities at aljout 2o° C. into almost
colourless rhombic plates if rapidly cooled down. When in a liquid
state, the crystals mostly occur in groups of long needles. The
colour of the substance in a melted state is brownish yellow ; at
moderate temperatures, and on standing in the air, it becomes still
darker in colour. It possesses a smell very much resembling cre^s.
It volatihzes at common temperatures, its vapour attacking the
eyes powerfully. Its vapour at higher temperatures, when carried
away by that of water, becomes more and more intolerable, pro-
ducing a very inflammatory effect on the eyes and nose, which is
more painful and permanent than that from acroleinc. It is insoluble
and sinks in water, but can be distilled in the vapour of it. Watery
solutions of carbonates and sulphites of the alkalies do not act on it.
Alcoholic solution of potash decomposes it by degrees on heating a
little, producing much iodide of potassium, some benzoic acid, and
an oily body that remains dissolved in the alcohol, which is not oil
of bitter almonds. Alcoholic and watery solutions of ammonia
change it slowly into iodide of ammonium and oil of bitter almonds.
Boiled with solution of nitrate of silver, it yields iodide of silver, and
a smell of oil of bitter almonds. Concentrated hydrochloric acid
changes it by degrees, becoming brown ; concentrated sulphuric acid
dissolves it on heating, with the separation of iodine.
In conclusion, the authors remark that the action of hydrochloric
acid on aldehyde may be regarded as consisting in the replacement
of two equivalents of oxygen by two of chlorine in one, two, or three
atoms of this body : thus. Aldehyde containing chlorine.
1 atom of aldehyde C, H, O., C,' H, CI,
2 „ „ C,H,0', C.H^O.Cl, Lichen's body.
3 „ „ C,.H,.0, C,,H,.O.Cl{^™;°Y'V'"'^' '^
' " '- ^- " 12 u 1 2 j^ aldehyde.
The action of hydriodic acid on oil of bitter almonds gives rise also
to a body derived from 3 atoms of this aldehyde, in which 2 (OJ is
replaced by 2(1,).
3 atoms of oil of bitter almonds, Oxyiodide of Benzaldehvdc,
C„II,,0, C„H„0,I,.
In the case of acroleinc, the action of hydrochloric acid is different ;
it combines directly with it, no elimination of water taking place. If
we conceive, however, that, in the action of this acid on common
aldehyde, the water which is there produced is the effect of a
further decomposition, tbcn we may readily suppose that, if this
further decomposition had taken place in the case of hydrochloric
acid and acroleinc, a body derived from two atoms of acroleinc,
and having O, replaced by CI,, corres])onding to the second term in
the combination of aldehyde and chlorine, would have been the re-
sult ; thus —
2 atoms of hvdrochlorate of acroleinc —
Ci,II,oO,Cl,— 2(11U) = C„II,0,C1,, corresponding to the
term C^ Hj, Oj Cl^ in common aldehyde.
314 Royal Society : —
There is a curious connexion which may be mentioned, in this
substitution of chlorine for oxygen in aldehyde, between the formula
of these bodies coutainmg chlorine, and those of the isomeric modi-
fications of aldehyde.
" Experiments on some of the Various Circumstances influencing
Cutaneous Absorption." By Augustus "Waller, M.D., F.R.S.
" On Spontaneous Evaporation." Bv Benjamin Guy Babington,
M.D., F.R.S. &c.
The object of this communication is to make known certain powers
of attraction and repulsion, hitherto, as far as I know, unnoticed,
which are possessed by soluble substances in relation to their solvent,
and which, in the case of water (the solvent here considered), are
measured by the amount of loss, on spontaneous evaporation, in the
weight of solutionsof different salts and other substances, as compared
with the loss of weight in water.
The force which holds together the particles of a vaporizable
liquid is gradually overcome, if that liquid be exposed to air, by
another force which separates, expands, and diffuses those particles
in the form of vapour ; and this separation takes place, even at a
common temperature, so rapidly, provided the surface be sufficiently
extensive, that an easy opportunity is afforded of determining the
loss of weight by a common balance.
A subject for investigation, possessing much interest, thus presents
itself; and in its pursuit some new and unexpected results are
encountered.
The method which I have pursued has been to expose to the
atmosphere, for a definite period, solutions of different salts, and also
pure water under like conditions of quantity and area, temperature,
atmospheric moisture, and atmospheric pressure.
Different salts and other soluble substances are thus found to
possess, when in solution, different powers of retarding or accelerating
evaporation, and hence, from its amount, as compared with that which
takes place in pure water, we can estimate the comparative value of
those powers.
The powers themselves being established as facts, the next point
is to endeavour to discover the cause or causes on which they depend j
and a wide field of inquiry is thus opened.
The following are the instruments which have been employed : —
1 . A balance, for one of the scales of which is substituted a flat
metal plate, six inches square, on which the vessels to be weighed
can be conveniently supported. This balance will turn sensibly at a
grain, even with a weight of 4 lbs. on either side.
2. A number of copper pans tinned within, all of the same size,
being precisely 5 inches square inside, with perpendicular sides
l^ths of an inch in height, also a number of earthenware pans of the
same dimensions, The area of 25 square inches has been chosen,
partly because this size is convenient for manipulation, and partly
because the results obtained can be easily represented in decimals.
This facility of decimal calculation would be of importance should
such pans come into general use as hygrometers, for which purpose
they are well adapted.
Dr. Babington on Spontaneous Evaporation. 315
3. Specific gravity bottles and counterpoises.
4. Thermometers of various degrees of delicacy and range, for
ascertaining freezing, temperate, and boiling points.
.5. Test tubes for use, in connexion with these thermometers, as
well in freezing mixtures as over the spirit lamp.
6. A barometer.
7. Various salts and other soluble substances, furnishing, when in
solution, the materials for examination.
The mode of procedure which I have adopted has been, to state
my facts in the form of propositions, and to prove each of these
propositions by experiments.
The propositions are as follows : —
1st proposition. — That in many aqueous solutions of salts and
other soluble substances evaporation is retarded, as compared with
the evaporation of water.
2nd proposition. — That in solutions of salts which retard evapora-
tion, that retardation is in proportion to the quantity of the salt
held in solution.
3rd proposition. — That different salts and other substances soluble
in water have different degrees of power in retarding its evaporation.
4tli proposition. — That the power of retarding evaporation does
not depend on the specific gravity of a solution.
5th proposition. — That in aqueous solutions of salts, the power of
retardation does not depend on the base, whether we compare solutions
containing like weights of the salt, or solutions of like specific gravities.
6th proposition. — That in aqueous solutions of salts, the power of
retarding evaporation does appear to depend upon the salt radical or
acid, although the retardation is not altogether independent of the
influence of the base.
7th proposition. — That salts with two equivalents of an acid have a
greater power of retarding evaporation than salts with one equivalent.
There are, however, exceptions.
8th proposition. — That there are some salts which, being dissolved
in water, do not retard its evaporation, and some salts which, so far
from retarding, actually accelerate evaporation.
The truth or probability of the foregoing propositions is established
by numerous experiments, but in this abstract I shall, for the sake of
brevity, only state the result of one or two experiments in proof of each.
The first proposition is proved by the fact that a solution of hvdro-
chloratc of soda in the proj)ortion of 480 grains to four measured
ounces of water, when cxj)osed under the conditions already stated to
spontaneous evaporation, lost only 33 grains in weight after twelve
hours' exposure — while four ounces by measure of water lost a3grains,
— and after twelve hours' further exposure lost only 109 grains, while
the water lost 1 74 grains ; that is, the water, as compared with the
solution, lost weight in the ratio nearly of 5 to 3.
The second proi)Osition is proved by the fact that a solution of
240 grains of hydrochlorate of soda in four ounces by measure of
water lost in twelve hours 73 grains by evaporation, while four ounces
by measure of pure water lost 81 grains, — this is in a proportion
of only about 8 of the latter to 7 of the former ; whereas, when double
316 Royal Society : —
the quantity or 480 grains of salt were dissolved, the pure water,
as compared with the solution, lost in the proportion of 5 to 3.
The third proposition is proved by the fact that a solution of 480
grains of nitrate of potassa in 4 ounces or 1920 grains of water lost
in twelve hours 95 grains ; while a solution of the same strength of
hydrochlorate of soda lost only 70 grains ; and again, a solution of
loaf-sugar, in which 480 grains were dissolved in 1920 gi'ains of water,
lost in 20 hours 1/5 grains, while a like solution of hydrochlorate of
soda lost only 117 grains.
The fourth proposition is proved by the fact that 480 grains of
gum-arabic dissolved in 1 920 of water had a specific gravity of 1 "072,
while a solution of hydrochlorate of soda of like strength had a spe-
cific gravity of ri49 ; after 1 \^ hours, the former had lost by eva-
poration 71 grains, while the latter had lost only 50 grains. Here,
therefore, the solution of the lighter specific gravity was less retarded
in its evaporation than the heavier solution. In contrast with this
fact, a solution of hydrochlorate of ammonia of 480 grains to 1920
grains of water, having a specific gravity of only r060, lost by evapo-
ration, in 8 hours and 44 minutes, 1 7 grains, while a like solution of
hydrochlorate of soda lost 24 grains. Here, then, the solution of
lighter specific gravity was more retarded in its evaporation than the
heavier solution. The conclusion is decisive that specific gravity has
no necessary connexion with the ])hfenomena.
The tifth proposition is proved by the fact that in the following
solutions of salts of potassa, all of the same strength (namely 1 salt
to 10 water), a difference in the amount of evaporation in each v.ill
be observed to have taken place ; and it must be borne in mind that
in solutions so weak we cannot expect that difference to be very great.
The reason for employing weak solutions was the necessity for
having all of the same strength, one in ten being the extent to which
the least soluble salt submitted to examination, namely, the sulphate
of potassa, will, at a low temperature, dissolve. grains.
Acetate of potassa lost in 35 hours .... 145
Bicarbonate of potassa lost in 35 hours . . . 131
Carbonate of potassa lost in 35 hours . . . 115
Ferro-cyanate of potassa lost in 35 hours . . 110
Hydrochlorate of potassa lost in 35 hours . . 98
Nitrate of potassa lost in 35 hours . . . . 117
Sulphate of potassa lost in 35 hours .... 132
Tartrate of potassa lost in 35 hours . . . . 151
The above solutions were next made all of one specific gravity,
namely TOGO, temp. 62° Fahr., instead of being all of one strength,
and the following is the result : — grains.
Acetate of potassa lost in lfi| hours . . ". . 4b
Bicarbonate of potassa lost in 16=1 hours ... 45
Carbonate of potassa lost in 1 65 hours . . , 35
Ferro-cyanate of potassa lost in 16| hours . . 41
Hvdrochlorate of potassa lost in 16| hours . . 32
Nitrate of potassa lost in 16| hours .... 39
Sulphate of potassa lost in 16| hours .... 42
Tartrate of potassa lost in 16i hours .... 43
Dr. Babington on Spontaneous Evaporation. 317
The sixth proposition is rendered probable by the following ex-
periment, in which solutions are employed of acetic, nitric, sulphuric,
and hydrochloric acids, combined respectively with potassa, soda,
and ammonia, in the proportion of lOU grains of the salt to 1000
grains of water. After the expiration of 10 hours and 20 minutes,
the solution of the three acetates lost respectively, for the potassa
salt 35 grs., for the soda salt 35 grs,, and for the ammonia salt
28 grs. In the solutions of the three nitrates, the loss was re-
spectively 24, 25, and 25. In the solutions of the three sulphates,
the loss was 30 grs., 37 grs., and 29 grs. respectively, while in the
solutions of the hvdrochlorates it was 17, 18, and 19 grains.
The seventh proposition is proved by an experiment in which a
solution of 100 grains of carbonate of potassa dissolved in 1000
grains of water is compared with a like solution of bicarbonate of
potassa. In ten hours the solution of the carbonate lost 45 grains,
while that of the bicarbonate lost only 36 grains. In comparing
like proportions and quantities of sulphate and bisulphate of potassa,
the respective losses in 13 hours were, for the former 53 grains, for
the latter 45 grains. Similar comjmrisous of the acetate and bin-
acetate of ammonia, phosphate and biphosphate, sulphate and
bisulphate of potassa, tartrate and bitartrate of soda show like
results. In the course of investigating this proposition it was
remarked incidentally that in all the salts examined, witli the single
exception of carbonate and bicarbonate of soda, the bin-acid solution
(the proportion by weight of salt to water being equal) is of less
specific gravity than the mono-acid solution, though possessing a
greater power of retarding evaporation.
The eighth proposition, which seems extraordinary and even
paradoxical, is proved by an experiment in which saii(7'afed solutions
of — 1, ferro-cyanate of potassa, 2, bitartrate of potassa, 3, sulphate
of copper, 4, chlorate of potassa, and 5, distilled water, were com-
pared. In 9 hours and 20 minutes, their losses by evaporation were
respectively 34 grs., 38 grs., 34 grs., 29 grs., and 29 grs., where we
perceive that in the chlorate of potassa solution there has occurred
no retardation at all, while in the following experiment, in which
120 grains of each of the salts examined were dissolved in 1200
grains of water, namely, — 1, solution of sulphate of copper, 2, solu-
tion of ferro-cyanate of potassa, .3, solution of carbonate of soda,
and 4, distilled water, the number of grains lost by evaporation after
15^ hours' exposure were, — 1, 120 grs.; 2, 113 grs.; 3, 106 grs.;
4, '103 grs.
It is thus perceived that in all the three solutions a more rapid
evaporation had taken place than in distilled water alone.
One or two other pro])ositions are in ])rocess of investigation.
The paper concludes with a table of the freezing-points, boiling-
points, and specific gravities, as well of weak as of saturated solutions,
of the salts which have been submitted to examination.
318 Geological Society : —
GEOLOGIC^iL SOCIETY.
[Continued from p. 238.]
February 1, 1860. — Sir C. Lyell, Vice-President, in the Chair.
The following communications Avere read : —
1. " On some Cretaceous Rocks in Jamaica." By Lucas Barrett,
Esq., F.G.S., Director of the Geological Survey in Jamaica.
On the north side of Plantain- Garden River, three miles west of
Bath, shale and limestone overlie conglomerate. The limestone
contains Inoceramus, Hippurites, and Nerincea. Higher up the river
similar fossiliferous limestone occurs in vertical bands, succeeded
by conglomerates, which separate it from massive porphyries.
On the medial ridge of mountains, also, at an elevation of 2500
feet above the sea, Hippurite-limestone, with black flints containing
Ventriculites, rests on porphyry and hornblende-rock. These igneous
rocks are interstratified with shales and conglomerates.
2. " On the Occurrence of a mass of Coal in the Chalk of Kent."
By R. Godwin-Austen, Esq., F.G.S.
This piece of coal was met with in cutting the tunnel on the
Chatham and Dover Railway, between Lydden Hill and Shepherds-
well. It weighed about 4 cwts., and was 4 feet square, with a thick-
ness of 4 inches at one part, increasing to 10 inches at another. It was
imbedded in the chalk, where the latter was free from faults. The
coal is friable, highly bituminous, and burns readily, with a peculiar
smell, like that of retino-asphalt. It resembles some of the Wealden
or Jurassic coals, and is unlike the true coal of the coal-measures.
Mr. Godwin-Austen stated his belief that during the Cretaceous
period some beds of lignite or coal of the preceding Jurassic period
lay near the sea-margin, or along some river, so as to be covered by
water ; and hence portions could be lifted off by ice, and so
drifted away (like the granitic boulder found in the Chalk at
Croydon) until the ice was no longer able to support its load.
3. " On some Fossils from the Grey Chalk near Guildford." By
R. Godwin-Austen, Esq., F.G.S.
In the cast of the body-chamber of a large Nautilus elegans, from
the Grey Chalk of the Surrey Hills, near Guildford, the author
found (the specimen having been broken up by frost) some lumps
of iron-pyrites, and numerous specimens of Aporrhais Parkinsoni,
with fragments of Turrilites tuberculatus, Aminonites Coupei, A.
vurians, and Inoceramus concentricus. These species are either rare
in the Grey Cltalk or not known to the author as occurring in this
bed ; and he believes that the specimens referred to were accumu-
lated in the shell of the Nautilus (possibly by the animal having
taken them as a meal shortly before death) at a different zone of sea-
depth to that in which the Nautilus and its contents sank and
became fossilized. Mr. Godwin-Austen referred to these specimens
as being indicative of the contemporary formation of different
deposits with their pecuHar fossils, at different sea-zones ; of the
transport of the inhabitants of one zone to the deposits of another ;
and as a possible explanation of the abundance of small angular
fragments of MoUusks, Echinoderms, and Crustaceans, in the midst
of the very finest Cretaceous sediment.
Mr. S. V. Wood on the Cretaceous Period. 319
4. " On the Probable Events which succeeded the Close of the
Cretaceous Period," By S. V. Wood, jun., Esq.
The object of this paper was to show that the close of the Secon-
dary period was followed by the formation of a continent having
a great extent from east to west, and at that time chiefly occu-
pying low latitudes ; that this direction of continent prevailed
throughout the Tertiary period ; and that in certain portions of the
southern hemisphere, particularly in Australia and New Zealand,
there have been preserved portions of the Secondary continent with
isolated remnants of the Secondary Mammalia and Gigantic Birds.
These conclusions were arrived at by a consideration of the direction
of the principal volcanic axes in the Secondary and Tertiary periods.
The Secondary continent was (the author considered) mainly influ-
enced in the northern hemisphere by volcanic axes which came into
action at the close of the Carboniferous, and continued through the
Secondary Period. These axes were that of the Oural, that of the
north of England prolonged into Portugal, and that of the Alleghanies,
having all a north and south direction, supervening upon volcanic
axes having a direction at right angles to them, which had prevailed
during the Newer Palseozoic period. From this circumstance an
inference was drawn that the Secondary continents had generally a
trend from north to south, governed by volcanic bands having
this direction ; while, as the Secondary formations indicate a great
extent of sea over the northern hemisphere, the bulk of the Secon-
dary continent lay in the southern hemisphere.
The elevation of the bed of the Cretaceous sea, it was inferred,
was due to volcanic forces acting from east to west ; and the author
adduced evidence of this action having become perceptible during
the later part of the Cretaceous period. He considered that the
direction of all the Post-cretaceous lines of volcanic action governed
the direction of the continent during the Post-cretaceous period,
and pointed out that these were all in an easterly and westerly
direction, coincident with the existing volcanic band which extends
from the Azores to the Caspian, and thence (with an interval of
intense earthquake-action between the Cas]nan and Bengal) extends
to the Society Isles. He concluded that they gave rise to a continent
extending from the Caribbean Sea to the Society Isles — manyreasons
uniting to show a land-connexion between America and Europe at
the dawn of the Tertiary period, the submerged continent of Oceanica
also indicating the easterly extension of Southern Asia ; and that,
since this continent receded to the north at the dawn of the Tertiary-
period before the inroad of the Nummulitic Sea (which stretched
from the south-east through Western Asia and Southern Europe,
and was, as the author conceives, the oceanic equivalent of the
Eocene basins of Europe) , the greater portion of the dcjiosits formed
in the interval between Cretaceous and Eocene times must be now
under the Southern Oceans.
The author then adverted to the circumstance that the recent
great wingless Birds and the nearest living affinities of all the
Secondary iMaramalia yet known occur only in the Southern hemi-
sphere. From this, and from some considerations as to the
320 Royal Institution : —
Vegetation, lie concluded that, -while parts of the Secondary conti-
nent yet remain in that hemisphere incorporated more or less into
the Post-cretaceous continent, other parts of it, such as Australia
and New Zealand, have remained isolated up to the present time to
an extent sufficient to preclude the migration of Mammalia and
wingless Birds. He inferred that the wingless Birds, excepting the
swift Struthionidse, have been preserved solely by isolation from the
Carnivora, which do not appear as an important family until the
Pliocene age; and he instanced the Gastrornis of the Eocene (which
had affinities with the Solitaire and Notornis) as evidence that the
apterous birds had survived until that period.
An inference was then drawn that the remains of the Secondary
continent, accumulated to the southward, caused cold currents to
flow to the southern shores of the Post-cretaceous continent, causing
the extinction of the bottom-feeding and shore-following Tetra-
branchiata, to which Mr. Wood attributes the destruction of the
Cestracionts which fed on them, and that of the marine Saurians
that fed on the Cestracionts. The preservation of the Dibranchiata,
on the contrary, was attributed to their being ocean-rangers. The
extinction of the Megalosauria he attributed to the effect produced
on vegetation by the alternation of dry seasons during the year,
brought about by a great equatorial extent of land, — the extinction
of the herbivorous Megalosauria, by this cause, involving that of the
carnivorous.
The author also alluded to the contiguitj^ of volcanos to the seas
or great waters, which he considered to admit of explanation by
every volcanic elevation causing a corresponding and contiguous
depression, which either brings the sea or collects the land-drainage
into contiguity with the volcanic region ; and in conclusion he
alluded to the law of natural selection and correlation of growth
lately advanced by Mr. Darwin, in the soundness of which he
asserted his belief.
ROYAL INSTITUTION OF GREAT BRITAIN.
March 9, 1860. — " On Lighthouse Illumination — the Electric
Light." By Professor Faraday, D.C.L., F.R.S.
The use of light to guide the mariner as he approaches land, or
passes through intricate channels, has, with the advance of society
and its ever increasing interests, caused such a necessity for means
more and more perfect, as to tax to the utmost the powers both of
the philosopher and the practical man, in the development of the
principles concerned, and their efficient application. Formerly the
means were simple enough ; and if the light of a lantern or torch
was not sufficient to point out a position, a fire had to be made in
their place. As the system became developed, it soon appeared
that power could be obtained, not merely by increasing the light,
but by directing the issuing rays : and this was in many cases a
more powerful and useful means than enlarging the combustion; leading
to the diminution of the volume of the former with, at the same time,
an increase in its intensity. Direction was obtained, either by the
use of lenses dependent altogether upon refraction, or of reflectors
dependent upon metallic reflexion, [And some ancient specimens
Prof. Faraday on Lighthouse Illumination, 821
of both were shown.] In modern times the principle of total
reflexion has also been employed, which involves the use of glass,
and depends both upon refraction and reflexion. In all these
appliances much light is lost : if metal be used for reflexion, a cer-
tain proportion is absorbed by the face of the metal ; if glass be used
for refraction, light is lost at all the surfaces w'here the ray passes
between the air and the glass ; and also in some degree by absorp-
tion in the body of the glass itself. There is, of course, no power
of actually increasing the whole amount of light, by any optical
arrangement associated with it.
The light which issues forth into space must have a certain
amount of divergence. The divergence in the vertical direction
must be enough to cover the sea from the horizon, to within a cer-
tain moderate distance from the shore, so that all ships within that
distance may have a view of their luminous guide. If it have less,
it may escape observation where it ought to be seen ; if it have
more, light is thrown away which ought to be directed within the
useful degree of divergence : or if the horizontal divergence be con-
sidered, it may be necessary so to construct the optical apparatus,
that the light within an angle of 60° or 45° shall be compressed
into a beam diverging only 15°, that it may give in the distance a
bright flash having a certain duration instead of a continuous light, —
or into one diverging only 5° or 6°, which, though of far shorter
duration, has greatly increased intensity and penetrating power in
hazy weather. The amount of divergence depends in a large degree
upon the bulk of the source of light, and cannot be made less than
a certain amount, with a flame of a given size. If the flame of an
Argaud lamp, |-ths of an inch wide and 1^ inch high, be placed in
the focus of an ordinary Trinity House parabolic reflector, it will
supply a beam having about 15° divergence : if we wish to increase
the effect of brightness, we cannot properly do it by enlarging the
lamp flame ; for though lamps are made for the dioptric arrange-
ment of Fresnel, whicli have as many as four wicks, flames 3^ inches
wide, and burn like intense furnaces, yet if one be put into the
lamp place of the reflector referred to, its effect would chiefly be to
give a beam of wider divergence ; and if to correct this, the reflector
were made with a greater focal distance, then it must be altogether
of a much larger size. The same general result occurs with the dioptric
apparatus ; and here, where the four- wicked lamps are used, they
are placed at times nearly 40 inches distant from the lens, occasioning
the necessity of a very large, though very fine, glass apparatus.
On the other hand, if the light could be compressed, the necessity
for such large apparatus would cease, and it might be reduced from
the size of a room to the size of a hat : and here it is that we seek
in the electric spark, and such like concentrated sources of light, for
aid in illumination. It is very true, that by adding lamp to lamp,
each with its reflector, upon one face or direction, power can be
gained ; and in some of the revolving lights, ten lamps and reflectors
unite to give the required flash. But then not more than three of
these faces can be placed in the whole circle ; and if a fixed light
be required in all directions round the lighthouse, nothing better
322 . Royal Institution,
has been yet established than the four-wicked Fresnel lamp in the
centre of its dio])tric and catadioptric apparatus. Now the electric
light can be raised up easily to an equality with the oil lamp, and
if then substituted for the latter, will give all the effect of the
latter ; or by expenditure of money it can be raised to a five or
tenfold power, or more, and will then give five- or tenfold eflfect.
This can be done, not merely without increase of the volume of
the light, but whilst the light shall have a volume scarcely the 2000th
part of that of the oil flame. Hence the extraordinary assistance we
may expect to obtain by diminishing the size, and perfecting the
optical part of the apparatus.
Many compressed intense lights have been submitted to the
Trinity House ; and that corporation has shown its great desire to
advance all such objects and improve the lighting of the coast, by
spending, upon various occasions, much money and much time for
this end. It is manifest that the use of a lighthouse must be never
failing, its service ever sure ; and that the latter cannot be interfered
with by the introduction of any plan, or proposition, or apparatus,
■which has not been developed to the fullest possible extent, as to the
amount of light produced, — the expense of such light, — the wear
and tear of the apparatus employed, — the steadiness of the light for
16 hours, — its liability to extinction, — the amount of necessary
night care, — the number of attendants, — the nature of probable
accidents, — its fitness for secluded places, and other contingent
circumstances, which can as well be ascertained out of a lighthouse
as in it. The electric spark which has been placed in the South
Foreland High Light, by Prof. Holmes, to do duty for the six win-
ter months, had to go through all this preparatory education before
it could be allowed this practical trial. It is not obtained from
frictional electricity, or from voltaic electricity, but from magnetic
action. The first spark (and even magnetic electricity as a whole) was
obtained twenty-eight years ago. (Faraday, PhilosophicalTransactions,
1832, p. 32.) If an iron core be surrounded by wire, and then moved
in the right direction near the poles of a magnet, a current of elec-
tricity passes, or tends to pass, through it. Many powerful magnets
are therefore arranged on a wheel, that they maybe associated very
near to another wheel, on which are fixed many helices with their
cores like that described. Again, a third wheel consists of magnets
arranged like the first ; next to this is another wheel cf the helices,
and next to this again a fifth wheel, carrying magnets. All the
magnet-wheels are fixed to one axle, and all the helix wheels are
held immoveable in their place. The wires of the helices are con-
joined and connected with a commutator, which, as the magnet-
wheels are moved round, gathers the various electric currents pro-
duced in the helices, and sends them up through two insulated wires
in one common stream of electricity into the lighthouse lantern.
So it will be seen that nothing more is required to produce the
electricity than to revolve the magnet-wheels. There are two
magneto- electric machines at the South Foreland, each being put in
motion by a two-horse power steam-engine ; and, excepting wear
and tear, the whole consumption of material to produce the light is
Intelligence and Miscellaneous Articles. 323
the coke and water required to raise steam for the engines, and car-
bon points for the himp in the lantern.
The lamp is a delicate arrangement of machinery, holding the two
carbons between which the electric light exists, and regulating their
adjustment ; so that whilst they gradually consume away, the place
of the light shall not be altered. The electric wires end in the two
bars of a small railway; and upon these the lamp stands. When the
carbons of a lamp are nearly gone, that lamp is lifted off and an-
other instantly pushed into its place. The machines and lamp have
done their duty during the past six months in a real and practical
manner. The light has never gone out through any deficiency or
cause in the engine and machine house ; and when it has become
extinguished in the lantern, a single touch of the keeper's hand has
set it shining as bright as ever. The light shone up and down the
Channel, and across into France, with a power far surpassing that
of any other fixed light within sight, or anywhere existent. The
experiment has been a good one. There is still the matter of ex-
pense and some other circumstances to be considered ; but it is the
hope and desire of the Trinity House, and all interested in the sub-
ject, that it should ultimately justify its^^fuU adoption.
XLII. Intelligence and Miscellaneous Articles.
BORACIC ACID IN THE SEA-WATER ON THE COAST OF CALIFORNIA.
nPHE following interesting paper on boracic acid in the sea-water
■■■ of the Pacific, on the coast of California, was read by Dr. John
A. Veatch before the California Academy of Natural Sciences. The
facts presented may lead to important results in various ways, and
deserve attention from scientific men. The Doctor said, —
The existence of boracic acid in the sea-water of our coast was
brought to my notice in July 1857. I had, in the month of Janu-
ary of the previous year, discovered borate of soda and other borates
in solution in the water of a mineral spring in Tehama county, near
the upper end of the Sacramento valley. Prosecuting the research,
1 found traces of boracic acid — in the form of borates — in nearly all
the mineral springs with which the State of California abounds.
This was especially the case in the Coast mountains. Borate of
soda was so abundant in one particular locality, that enormous
crystals of that salt were formed at the bottom of a shallow lake, or
rather marsh, one or two hundred acres in extent. The crystals
were hexahedral with beveled or replaced edges, and truncated
angles ; attaining the size, in some cases, of 4 inches in length by
2 in diameter, forming splendid and attractive specimens. In the
same neighbourhood, a cluster of small thermal springs were observed
holding free boracic acid in solution. A few hundred yards from
these a great number of hot springs, of a temperature of 212° Fahr.,
rose up through the fissures of a siliceous rock. These springs held a
considerable quantity of borax, aswell as free boracic acid. Manyother
localities furnished similar indications, but in a less extensive form.
In progress of the examination I found that the common salt
(chloride of sodium) exposed for sale in the San Francisco market,
and which, it was understood, came from certain deposits of that
824 Intelligence and Miscellaneous Articles.
article on the sea-margin in the southern part of the State, also fur-
nished horacic acid. I was led to attribute it to the fact of mineral
springs emptying into the lagoons furnishing the salt. It was there-
fore a matter of no small surprise when, on a visit to the localities,
I found no trace of acid in any of the springs in the adjacent district.
This led to an examination of the sea-water, and a detection of an
appreciable quantity of boracic acid therein. It was at Santa Bar-
bara where I first detected it, and subsequently at various points,
from San Diego to the Straits of Fuca. It seems to be in the form of
borate of soda, and perhaps of lime. The quantity diminishes towards
the North. It is barely perceptible in specimens of water brought
from beyond Oregon, and seems to reach its maximum near San Diego.
This peculiarity seems to extend no great distance seaward.
Water taken thirty or forty miles west from San Francisco gave no
trace of acid. In twelve specimens, taken at various points betwixt
this port and the Sandwich Islands, furnished me by Mr. Gulich, of
Honolulu, only that nearest our coast gave boracic acid. In ten
specimens kindly fui-nished me by Dr. W. O. Ayres, taken up by Dr.
J. D. B. Stillman, in a trip of one of the Pacific mail steamers from
Panama to this place, no acid was observed south of theCortez Shoals.
I have not as yet been able to obtain specimens of w'ater south of
San Diego, nearer the shore than the usual route of the mail steamers.
Neither have I been able to test the breadth of this boracic acid belt
any further than the fact above stated, of no acid being found at the
distance of thirty or forty miles west from the Golden Gate. I
think it probable that it is confined within the submarine ridge run-
ning parallel with the coast, the southern portion of which is indi-
cated by certain shoals and island groups. The source of the acid
is undoubtedly volcanic, and the seat of the volcanic action is most
likely to exist in this submerged mountain range. It strengthens
the probability of the eruptive character of the Cortez Shoals.
I hope hereafter to be able to make more accurate and extended
examinations, unless some one more capable of doing justice to the
subject should take it in hand. With this view, I solicited the at-
tention of Dr. J. S. Newberry to these facts, while he was in this
city, on his way to join Lieut. Ives's Colorado Exploring Expedition,
hoping he might think it worthy of investigation during his stay on
this coast. With the same view, I now submit them to the Academy.
— Journal of the Franklin Institute for February 1860.
A NEW KIND OF SOUND-FIGURES FORMED BY DROPS OF A LIQUID.
BY F. MELDE.
If a drinking-glass, or a funnel of about 3 inches diameter at
the edge, be filled with water, or alcohol, or ether, and a strong note
be made by dra\\-ing a violin-bow on the edge, a sound figure will
be formed on the surface of the liquid, consisting of nothing but
drops of liquid. If the vessel gives the fundamental note, the figure
forms a four-rayed star, the ends of which extend to the four nodal
points ; but if the note which the vessel gives be the second higher,
the star will be six-rayed ; and if the vessel gives still higher tones,
other more numerously rayed stars are produced. — PoggendorfF's
Annalen, January 1860.
THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
MA Y I860.
XLIII. Crystallographic Notices. By W. H. Miller, M.A.^
F.R.S., Professor of Mineralogy in the University of Cambridge^.
On the Employment of the Stereographic Projection of the
Sphere in Crystallography.
IN the Philosophical Magazine for July 1859, it is shown that
the properties of anharmonic ratios may be used with
advantage in constructing the gnomonic projection of the sphere
by which Neumann represents crystalline forms, and also in
constructing the projection applied to the same purpose by
Quenstedt. I was unable, at that time, to extend the method
to the representation of crystalline forms, according to Neumann's
method, by the stereographic projection. Subsequently, however,
I have ascertained that it is equally applicable to the stereographic
projection, leading to a construction by which the centre of the
projection of any zone-circle may be readily determined. Hence,
having given the centre and radius of the primitive, the radius
of the projection of a zone-circle may be found, being the hypo-
thenuse of a right-angled triangle one side of which is the radius
of the primitive, and the other side the distance of the centre of
the projection of the zone- circle from that of the primitive. The
construction for finding the magnitude of a line or angle from
that of the anharmonic ratio into which it enters, will be found
in art. 13 of the paper in the Philosophical Magazine referred
to above.
Let P, Q, R, S be the centres of the projections of four zone-
circles K P, K Q, K R, /C-S^ passing through the point K ; K the
projection of K; efg, pgr the symbols of K P, KR; hkl,
uvio the symbols of the poles Q, S in the zone-circles K Q, A'^.
* Communicated by the Autlior.
Phil Mag. S. 4. Vol. 19. No. 128. May 1860. Z
326 Prof. Miller's Crystallographic Notices.
The angle which the distance between the centres of any two of
the circles subtends at K, is equal to the angle between the
corresponding originals. Therefore, since the anharmonic ratio
of P, Q, R, S is the same as that of K P, K Q, K R, K S,
PQ RS _ eh+fk+ffl pu + gv + rw
RQ PS ~ph-i-qk + rl eu+/v+gw '
Let the zone-circle Q S meet the
zone-circles KP, KR in the poles
P, R. Let T be the centre of the
projection of the zone-circle Q S ; ^ Q
T P, T Q, T R, T S the loci of the centres of projections of great
cu-cles the originals of which pass through P, Q, R, S respectively.
Therefore, since the anharmonic ratio of the lines T P, T Q, T R,
T S is the same as that of the points P, Q, R, S,
sin PTQ sin RTS _ eh+fk+gl pu + gv + rm
sin RTQ sin PTS ~ ph + gk + rl eu +fv -\-gw '
The symbol of any zone-circle may be used to denote the
centre of its projection, and the symbol of any pole may be used
to denote the straight line which is the locus of the centre of the
projection of a great circle passing through it.
Let D, E, F, G be the centres of the projections of four zone-
circles, no three of which are in one straight line ; H the inter-
section of D E, F*G ; M the intersection of the circles having
their centres in JD, E ; N the intersection of the [circles having
their centres in F, G. The straight line T) E is the locus of the
centres of the projections of great circles passing through tlie
original of M ; F G is the locus of the centres of the projections
of great circles passing thi-ough the original of N. Therefore
H is the centre of the projection of the great circle which is the
original of M N. Hence, if the centre of the projection of a
zone-circle be denoted by the symbol of the original, and the
line joining any two centres be denoted by the symbol of the
pole in which the originals intersect, the rule for finding the
symbol of a zone-circle from the symbols of two poles in it, or
for finding the symbol of the pole in which two zone-circles
intersect, from the symbols of the zone-circles, may be applied
to find the symbol of a line fi'om the symbols of two centres
through which it passes, or to find the symbol of the intersection
of two lines each of which joins two centres, from the symbols
of the lines.
The expression
eh +fk +gl pu + gv + rw
ph + qk + rl eu+fv+gw'
where efg, pgr Are the symbols of two zone-circles K P, K R,
Prof. Miller's Crystallographic Notices. 327
or two straight lines K P, K 11, and h kl, uv w arc the symbols
of two poles Q, S or of two points Q, S, may be conveniently
denoted by K P, Q . K R, S (or Q, K P . S, K R), which shows
how the indices of K P, K R, Q, S are combined in the nume-
rator. This notation is especially useful when the indices of K P,
Q, K R, S are not denoted by letters. When they are denoted
by letters, it suggests efg, hkl.pqr, uvwasa, convenient ab-
breviation of the preceding expression.
Let D, E, F, G be four centres of projections of zone-circles,
no three of which are in one straight line, and of which the
symbols are known ; T the centre of the projection of any other
zone-circle. Let H be the intersection of D E, F G. The sym-
bols of D, E being given, that of D H is known. When the
symbol of T is given, that of D T may be found. The angle
G D T is then given by the equation
sin GDH sin FDT
smFDH smGDT '
In like manner the angle G E T is given by the equation
sinGEH sinFET pT.TTpT.rn
smFEHsmGET ' '
Hence the position of T is de-
termined.
When T is given, the ratios
of the indices of the zone-circle
the projection of which has T for^^
its centre may be found from the preceding equations.
Having given the symbol of a pole, to find the centres of the
stereographic projections of any two great circles which intersect
in its projection Q.
Let the locus of the centres of the projections of great circles
passing through Q, meet D E in V, F G in W, and G D in U.
The symbol of UWis the same as that of the original of Q.
From this, and the symbols of D, E, F, G, those of H, U G, U W,
can be obtained. The points V, W arc then given by the
equations ttD EV
5g5-jjy = H.UG.E,my,
HG FW
FG HTV = H, UG . F, UW.
When Q, the projection of any pole, is given, let the straight
line U W passing through the centres of the projections of any
two great circles intersecting in Q, meet 1) E, F G in V, W.
Then the preceding equations give the ratios of the indices of
U W, or of the original of Q.
Z2
328 Prof. Miller's Crystallographic Notices.
It is easily seen that the centre of the stereographic projection
of a zone-circle is Quenstedt's projection of the corresponding
zone-axis, the nearer pole of the primitive being the fixed point
of Quenstedt's projection ; and that the straight line through the
centres of the stereographic projections of two zone-circles, is
Quenstedt's projection of the face having its pole in the inter-
section of the two zone-circles.
On the Measure of the Dihedral Angles of Crystals.
Euclid's definition of a dihedral angle takes no account of the
difference in the nature of the matter on opposite sides of the
planes forming the dihedral angle; therefore, though sufficient
for the purposes of geometry, it must be modified to suit the
requirements of crystallography. The dihedral angle made by
two faces of a crystal, considered as planes separating matter of
one kind from matter of another kind, may be measured in two
different ways ; either by the angle between normals to the faces,
drawn from any point within the crystal towards the faces ; or,
by the supplement of this angle. The latter measure, which
was unfortunately adopted by the earlier crystallographers, leads
to the preposterous conclusion, that if two plane mirrors be
placed back to back, with their faces perpendicular to a given
straight line, the angle which the face of one mirror makes with
itself is 180°, and the angle which the face of one mirror makes
with that of the other, is 0°, though the mirrors are in the most
dissimilar positions, having their faces directed to points dia-
metrically opposite. It is scarcely possible that this measure
would have been adopted if the invention of the Reflective
Goniometer had preceded the crystallographic researches of Rome
de I'Isle. In order to give an angle by a single reading, in
accordance with Carangeot's goniometer, Wollaston repeated the
numbering of the graduation in each semicircle (a source of
ambiguity in the recorded observations), instead of numbering
up to 360°, as is usual in circular instruments, and introduced
two stops and a spring which permitted the circle to turn only
in a direction contrary to that of the numbering, and enabled
the circle to be fixed nearly at 0° and 180°. This contrivance
was but partially successful ; for it only gave the angle between
two faces one of which was observed at 0° or 180°, leaving the
other dihedral angles to be obtained by subtracting the difference
between the corresponding readings from 180°; and in the most
carefully constructed instruments the adjustment of the stops
was too uncertain to fix the zero of the vernier at 0° or 180°,
without leaving an error too large to be neglected. In the best
goniometers now constructed the stops are omitted, and the gra-
duation is numbered up to 3G0°. The difference of the readings
Prof. Miller's Crystallographic Notices. 329
of the circle, corresponding to the observations by reflexion from
any two faces of a crystal, gives the angle between normals to
the faces, from a point within the crystal. The data employed
in calculating dihedral angles, and the results of the calculations,
are expressed in the same measure. The supplement of the
angle between normals to two faces is nowhere used as the
measure of a dihedral angle, except in the lists of angles which
accompany the descriptions of mineral species. An angle taken
from one of these lists cannot be compared with the direct result
of observation or of calculation, without first subtracting one or
the other of them from 180°. In order to avoid the needless
trouble of subtracting angles from 180°, which from its frequent
occurrence becomes extremely irksome, the editors of the last
edition of Phillips's 'Mineralogy' ventured to measure a dihedral
angle by the angle between normals to the faces containing it,
from a point within the crystal. That they have not been over
hasty in breaking through an inconvenient and unphilosophical
convention, may be gathered from the fact that the same defini-
tion has since been adopted by Beer, Dauber, Grailich, Guiscardi,
Handl, Hess, v. Lang, IMurmann, Rotter, Schroder, Sella,
de Senarmont, and v. Waltershausen.
The use of the angle between normals to the faces as the
measure of the dihedral angle they make with each other, is
attended by some incidental advantages. It enables the reader
to apprehend more clearly the relative positions of the faces by
inspection of the recorded angles ; employs fewer figures ; and
in the descriptions of twin crystals, marks re-entering angles by
giving them negative values.
On the Cleavages of Rutile.
In Breithaupt's 'Mineralogy' rutile is described as having
cleavages parallel to the faces of the forms 100 and 110, with
traces of cleavage parallel to the faces of the form 1 ] 1. The
last of these has been overlooked in the mineralogical treatises
which have appeared since 1847, the date of the last volume
published of Breithaupt's work. Three crystals of rutile forming
part of the Brooke Collection, now in the Mineralogical Museum
of Cambridge, exhibit the cleavage 111 very distinctly. In two
of them it is interriipted by traces of cleavage parallel to the
faces of the form 3 2 1. I have also observed the cleavage 111
in two crystals of rutile in my own possession, and in one of
them, rather obscure traces of the cleavage 3 21. The symbol
1 1 1 is used to denote the simple form in which 111, 111
= 95° 20'; 111, Ill = 56°52'. 321, 001 = 6G°42';
321, 231=20° 46'; 321, 11 1=26° 0'.
330 On the Composition of Water from the Coal-strata.
On the doubly -refractive character of Thermophyllite.
Some crystals of thermophyllite, a mineral of which an analysis
by Mr. Northcote was published in the Philosophical Magazine
for October 1858, were too imperfect to be measured, or to
exhibit coloured rings when examined with a polarizing instru-
ment having three lenses of equal focal length, resembling the
instrument contrived by the Astronomer lloyal (Cambridge
Philosophical Transactions, vol. iv. p. 199). Norrenberg^s
newest polarizing instrument, in which the focal length of the
eyepiece is many times that of the other two lenses, or com-
binations of lenses (Grailich, Krystallographisch-optische Unter-
suchungen, p. 43), though it does not allow the positions of the
optic axes to be determined with much accuracy, permits the
use of a proportionably smaller slice of crystal. With an instru-
ment constructed on this principle it was not difficult to make
out the existence of two optic axes in thermophyllite, making
with each other an angle of about 22° 30' in air. The position
of the bisectrix with respect to the cleavage could not be measured
on account of the curvature of the latter. It appeared to be
perpendicular to the cleavage. It is therefore probable that the
ciystals belong to the prismatic system.
XLIV. On the Composition of Water obtained from the Coal-
strata, Bradford Moor, Yorkshire. By F. A. Abel, Esq.^
THE analysis of a sample of water from the above source
was undertaken a short time since with the view to ascer-
tain whether it was adapted to general domestic purposes. The
results furnished by the examination appeared of sufficient in-
terest to warrant their publication.
Two samples of the water collected at the mouth of a coal-pit,
at an interval of about one month (the separate analyses of which
furnished thoroughly concordant results), were submitted to me
officially for examination by Lieutenant Colonel Hamley, Com-
manding Royal Engineer at York, who informed me that the
water, which is highly esteemed in the neighbourhood for drink-
ing and culinary purposes, is raised from coal-pits, at a depth
of about 200 feet beneath Bradford Moor, — an abundant and
regular supply being obtained.
The specific gravity of the water was 100078 at 60° F. Its
reaction was powerfully alkaline, and its flavour was brisk and
agreeable.
The proportion of solid matter obtained on evaporation
* Communicated by the Author.
Mr. J. Cockle's Note on the Remarks of Mr. Jerrard. 331
amounted to 44' 1 grains in an imperial gallon, of which by far
the largest proportion consisted of carbonate of soda.
The alkalinity of the boiled water was determined by means
of standard sulphuric acid, and found to be equivalent to a pro-
portion of 30"76 grains of carbonate of soda in an imperial gallon.
The result obtained by the direct determination of the carbonic
acid, corresponded accurately to the proportion required by theoiy
to hold in solution the whole of the lime and magnesia in the
water, and to form bicarbonate with the amount of soda repre-
sented by the number above quoted.
The following statement represents the proportions of the
various constituents existing in solution in an imperial gallon of
the water : —
Bicarbonate of soda .... 43*53
Sulphate of soda 7*50
Chloride of sodium .... 1*34
Sulphate of potassa .... 0'31
Phosphate of lime .... trace
Carbonate of lime .... 1*90
Carbonate of magnesia . . . 0-80
Organic matter 1*20
Carbonic acid, holding the carbonates of lime and magnesia in
solution, 1'25 grain = 2*642 cubic inches at 60° F.
The absence of nitric acid, ammonia, silicic acid, alkaline sul-
phides, and oxide of iron was established by special examinations.
XLV. Note on the Remarks of Mr. Jerrard.
By James Cockle, Esq.*
THE inverses of the rational functions, say R, by which one
of two similar functions is expressed in terms of the other
are themselves rational, and the inverses of those by which one
root of an irreducible equation is (if so expressible) expressed
rationally in terms of another are also themselves rational. And
if 3, 6 be similar functions of which 3,, d^ and Sgj ^o ^^'® ^^^'
responding values, and if moreover H be the root of an irredu-
cible equation one root of which. Eg, is a rational function, say
r, of another, Hj, wc find
^2 = RSa = RrH 1 = RrR - ' 6'„
in other words, that 0^ is a rational function of ^p Conse-
quently if the equation in 6 is not an Abelian, neither is the
equation in H an Abelian.
Again : if a rational equation be reducible, any rational trans-
formation involving only one root gives rise to a reducible trans-
* Communicated by the Author.
332 Mr. J. Cockle's Note on the Remarks of Mr. Jerrard.
formed equation. And, since
W^^+W;^^^^^, and 9^ + 6^, and 6^0^
arc similar functions, if the 15-ic in the V of Mr. Jerravd be
reducible to cubic factors, the 15-ics in ^, + ^4 and 6^6^, that is
to say in ^ and h, are so reducible. But this is not the case.
Under the most favourable circumstances in which we can form the
cubic in ^, the coefficients are unsymmetric. And the structure
of the 15-ic in 7, which is reducible to a quintic and a 10-ic
equation, discloses no means of attaining a cubic with known
coefficients. The most favourable combinations, those of the
forms '^rfi-jx.c,, 'y^^a^, or yrfici/3.^*, are unsymmetric.
Further : the coefficients of the cubics of Mr. Jerrard are (see
arts. 69, 94, 109, and 110 of his ' Essay t ') expressible rationally
in terms of x^, x^, . . x^, and the doctrine of similar functions
shows that they are either symmetric or incapable of evaluation
save by a quintic. In the former case the five cubics are iden-
tical ; in both cases the results are illusory. It is a significant
fact that the soluble form of art. 96 of my ' Observations,' for
which the sextic in t degenerates into a cubic, is not irreducible J.
The 'Essay' of Mr. Jerrard is of surpassing interest, but
these objections to the particular portion of it which relates to
the finite solution of quintics seem to me to be fatal. A deep
admirer of his researches, and indisposed to regard as established
conclusions in which Mr. Jerrard does not concur, I may be per-
mitted to express a hope that the promised sequel to the ' Essay *
will not be long delayed.
Lastly : how can each one of the system of five cubics men-
tioned in art. 110 (p. 84) of Mr. Jerrard's ' Essay' be separated
fi'om the rest save by a quintic ? How can this quintic be solved
unless it be an Abelian ? And how can it be an Abelian if the
given quintic be not an Abelian ? "What evidence is there that
the four N's vanish as alleged by Mr. Jerrard ?
4 Pump Court, Temple, London, E.G.,
AprU 7, I860.
* Mr. Harley has completely determined all the ^ and u functions. I
have selected these combinations from his values, kindly communicated
to me.
t Part I. 1858; Part II. 1859. Taylor and Francis.
X See a solution, for the case Q=:l, by Mr. Stephen Watson in the
' Educational Times,' April 1860. Neither of the standard particular sol-
vable forms
x'-^x^+^=0, aS_5a^+2=0
to which I have been conducted is irreducible.
[ 333 ]
XLVI. Note on some Prismatic Forms of Calcitefrom LnganurCj
County of Wicklow. By William K. Sullivan*.
IN the first edition of his Traite de Mineralogie (Paris, 1801),
Haiiy distinguished three kinds of prismatic carbonate of
lime: — 1. Chaux carbonatee prismee, ah'eady described by Rome
de Lisle, and which Haiiy supposes to be derived, in his mole-
cular theory of decrements by the law d^. According to this, it
would be the prism produced by modifying planes placed upon
the lateral edges of the primitive rhombohedron. The second
he calls chaux carbonatce imitative, and considers to be the prism
obtained according to the law e^ by planes on the lateral angles
of the primitive. The third, which had also been before de-
scribed by De Lisle, he named chaux carbonatce prismatique,
and considered to be also derived according to the law e^. He
mentions four varieties of this form : a, alternating — having
three alternate wide faces and three intermediate narrow ones ;
b, compressed — with two opposite faces larger than the other
four; c, widened — with four faces wider than the remaining
two ; and d, lamelliform — in very short [i. e. in tabular) prisms.
Of the crystals of this form he says, " In certain crystals the
extremities are of a dull white, while the intermediate part is
transparent. In others the opake part is situated towards the
axis and surrounded by a transparent envelope. The bases of
a few exhibited concentric hexagons, and one could even ob-
serve the extremity of a small internal prism, rising above the
whole prism."
The forms he calls imitative and prismatic being obtained by
the law e^, contain the same prism ; the prismatic faces which
have been observed among the varieties of calcite belong,
therefore, to one or other of those prisms. Dufrenoy, who uses
the nomenclature of Haiiy, as modified by Levy and himself,
represents the faces of the first prism, or that on the edges of
the rhombohedron, by the symbol d^ {u of Haiiy), and the pris-
matic, or that on the angles, by e^ (c of Haiiy). Of course each
of these prisms is completed by the modification a^ on the
summit angle, which produces the horizontal plane forming the
base.
According to the German crystallographic methods, prisms are
looked upon as mere limiting'forms. Mobs and Haidinger con-
sider d' to be the limiting form of the pyramids, the former
expressing it by the symbol P + co and the latter by oo P, which
is the one adopted by Zippe in his summary of all the observed
forms of carbonate of lime f. The second prism, e^, is considered
* From the Atlantis, No. V. p. 176. Communicated by the Author,
t Uebersicht der KrystaUgestalten des rhomboedrischen Kalk-Haloids,
334 Mr. Sullivan on some Prismatic Forms of
to be the limiting form of the rbombohedi-on, and is represented
by Mobs by the symbol 11+ go, and by Haidinger by co R.
Zippe also adopts the latter.
According to Haiiy d' or ooP is rare, and Dufrenoy states
that only some examples are known. According to Zippe, it is
frequent enough in combination as a secondary form, butseldomcr
as the dominant form. Surmounted by the primitive rhombo-
hedron (R or P), it is noticed by Dufrenoy as "a very rare ex-
ample of the prism on the edges, associated with the primitive
rhombohedron*" from Cumberland. He also mentions another
in which Z*' or ^R' (the equiaxe of Haiiy) replaces P or R, but
does not give the locality. Further on he notices a third ex-
ample from the Samson mine in the Hartz, in which the hori-
zontal edges of the prism are truncated by rudimentary planes
of the pyramid.
The prism ooR or e^, although comparatively rare as a simple
form, is very frequent in combination ; according to Dufrenoy,
indeed, it is the only one found complete. A little before, he
says that it is of a milky whiteness, and almost always opake.
The base sometimes bears strise parallel to the edges, which are
indications of cleavage. Examples of ooR surmounted by ~W
or b' from the Hartz, Cumberland, and the department of I'Isere,
have been described.
The position of the rhombohedrons surmounting the prisms is
different in each kind. In goP the surmounting rhombohedral
faces lie so that the edges of combination with the prismatic
faces coincide with the lateral edges of the rhombohedron. In
ooR the edges of combination in three alternate faces are hori-
zontal ; the truncatures at either end of the prism alternating,
so that each face of truncature is parallel to one at the opposite
end. The directions of the cleavages correspond perfectly with
the dispositions of the modifying planes, so that every alternate
basal edge of the prism coR or e^ may be removed by cleavage
with the greatest facility, by which a prism surmounted by the
faces of the rhombohedron may be obtained.
Although the prismatic faces goR are sometimes dull, they
always, at least in all the crystals which I recollect to have seen,
possess more lustre than the faces ooP associated with them.
The former are, indeed, usually veiy bright in transparent
crystals. This circumstance is noticed by Dufrenoy, who, in
speaking of the example of ooP or {J}) with pyramidal trun-
catures of the lateral edges, from Samson mine in the Hartz,
von F. X. M. Zippe. — Denkschriften der Kaiserl. Akademie der Wissen-
schaften. Mathematisch-naturwissenschaftliche Classe, Bd. iii. 1st Lief,
p. 109,
* Traite de Mineralogie, par A. Dufrenoy. 2 ed. tome ii. p. 297.
Calcite from Luganure. 335
says that the faces arc dull and somewhat rough, as is frequently
the case with those prisms [" les faces en sont mates et un pcu
raboteuses, circonstance frequente pour le second prism {i. e. d})
a six faces ^'] . The difference in lusti'e between the faces of the
two kinds of prisms is characteristically seen in the dodecagonal
prisms (chaux carbonatee peridodecaedre of Haiiy), which is
the combination coR, coll, oP {d} e^ a}) ; the faces ooR (e^) are
always very much more brilliant than ooP {d}). This difference
of lustre is one of the distinctions relied upon to distinguish the
faces of the two kinds of hexagonal prisms from one another.
Dufi-enoy also notices this difference between the two kinds of
prismatic faces in the twelve-sided prisms.
Several forms of the rhombohedral prism occur at the Lu-
ganure mines. County of Wicklow, which are worked for galena
in a veinstone consisting chiefly of quartz, in a granite country.
Among these may be mentioned ooP, oR {d^, a}), consisting of
small hexagonal prisms, wdth very bright prismatic faces. One
half of the prism is hyaline, and the other opalescent ; the base
oR is dull. Another variety of the same form also occurs, con-
sisting of crystals one centimetre high, and with basal edges one
centimetre long. Each crystal has a sort of rude triangular
prismatic milky nucleus, surrounded by a perfectly hyaline enve-
lope, reminding one of the description of Haiiy given above.
Owing to the number of cleavage planes, some crystals are not
transparent. The face oR is in most instances peculiarly
striated, in others it is, as it were, coated with a thin porcela-
neous layer. These crystals may be easily cleaved parallel to
the alternate basal edges, which are sharp, and without any
trace of modifying planes. The form oR, gcR (a*, e^) also occurs
in beautiful hexagonal plates, w^ith very bright prismatic faces,
and composed of exceedingly thin alternating layers of white
opake, and hyaline matter, the base oR being always opake,
dull, but beautifully white. Haiiy's description of the prismatic
kind embraces this variety likewise ; in fact, the specimens
from Luganure here described illustrate perfectly Haiiy's de-
scription.
I have latelj', however, met with another form, consisting of
hexagonal plates, of from one millimetre to one and a half thick,
with basal edges of from five to twenty millimetres. The base
has a bright nacreous lustre, much brighter than what I have
ever seen in any other specimen ; striated and uneven, in conse-
quence of the lapping of smaller plates. The most of the tabular
])risms are, in fact, compound twins to the base oR («^). Some
twins also occur to the faces of the prism, and finally, to a
rhombohedi'on. It is owing to this twhi structure that the
crystals are not generally transparent ; for in thin plates they are
336 Mr. Sullivan on some Prismatic Form^ of
perfectly hyaline. Except for the difference of form^ a mass of
these crystals, resting on crystalline quartz, resembles, in a strik-
ing manner, a mass of large crystals of chlorate of potash. Layers
of growth in the direction of the secondary axes can be observed
in some of the prisms ; in many of these the outer shell, about
one millimetre thick, is frequently free from indications of
cleavage, and perfectly transparent. The prismatic faces are dull,
exactly like the appearance of white wax when sufficiently thin
to be translucent; they are also uneven. These faces exactly
resemble those of the prism ccP (f/'), in specimens which I have
seen from Andreasberg. On this account, I concluded, at first
sight, that I had the combination oP, cx:P, which would be not
merely rare as an example of the pyramidal prism, but still more
so as a tabular form of it, in which the base would impress its
character upon the crystal, and of which I have not seen
any example recorded. I found, however, that the alternate
edges were modified by rudimentary facets of a rhombohedron,
which was placed in the same position, as regards the faces of
the prism, that I have before mentioned as characteristic of ocR.
The basal edges not modified were easily removed by cleavage.
I found the modifying facets to be those of the rhombohedrou
i R' or b\
Associated with the crystals just described, were sometimes
found white opake crystals, like those from Andreasberg, and
others three or four millimetres thick, upon which were rudi-
mentary facets of a scalenohedron. I have not been able to get
any good specimens of these varieties.
It may be worth while to enumerate, from Zippe's excellent
memoir, the tabular prismatic forms which have been hitherto
observed, with a view of determining the exact position of
the example just described in the series. They are as follow: —
1. oR, 2P, ocR, ooP {a\ e^, e^, d^) figured by Levy*.
2. oR, ^R', GcR (fli, b^, e^) white tabular crystals from Wear-
dale in Durham.
3. oR, GcRj coP {a}, e^, d^) from Andreasberg.
4. oR, 2R', ccR, acP {a}, e^, e^, d^) from Andreasberg.
5. oR, :^R', ^ R, GoP from Andreasberg.
6. oR, ocR from Andreasberg, Marienberg, Schneeberg,
Joachimsthal, and Schemnitz.
The last-mentioned form from Luganure, which is oR, ocR,
■|R' (a', e^, h^), approaches nearest to TS'o. 6, from which it differs,
so far as can be expressed by a formula, only by the rudimentary
rhombohedral facets. If the faces -^R' became so developed as to
* Description cfune collection de min&aux formee par H. Heuland, ^c,
Londres, 1837, fig. 8/.
Calotte from Luganure. 337
render the faces ooR, subordinate to them, it would pass into the
form No. 2 from Wcardale. I have, indeed, found a few imper-
fect crystals from Luganure, in which the prismatic faces are only
rudimentary, the outline of the tabular crystal being rhombo-
hedral.
Although, as I have above observed, the prismatic faces ooR
are sometimes dull, the combination of brilliant nacreous oR
faces with wax-like prismatic faces exactly like those character-
istic of the faces coP is, so far as I am aware, extremely rare.
In the mineralogical collection of the Museum of Irish Industry
there is a specimen from Andreasberg, in tabular crystals some-
what thicker than those from Luganure, which I have described.
The same kind of rudimentary facets occur in the alternate
basal edges. I have not had an opportunity of determining
whether they belong to gR' [b^]. The prismatic faces have the
wax-like dullness of the Luganure specimens ; but the crystals
are opake, and the faces oR are dull, and in other respects
very different in appearance from those just mentioned. In the
same collection, characteristic specimens of the other forms from
Luganure which I have mentioned are to be found, as well as
of several others, of which I have not yet been able to procure
specimens*.
* Tt is to be regretted that the descriptions, both crystallographic and
mineralogical, of the minerals from Irish localities, which are to be found
in Irish collections, have not been more generally published. It is only by
the careful study of the conditions under which certain forms of minerals
are found, the first element of which is a faithful record of the circumscribed
localities in which they occur, that we can hope to arrive at a solution of
the important problem in molecular physics — the causes which produce
modifications of form in bodies. The ' Manual of the Mineralogy of Great
Britain and Ireland,' by Robert Philips Greg, F.G.S., and William G.
Lettsom, forming one of the admirable series of Manuals published by
Van Voorst, is a most praiseworthy step in this direction. It is with regret,
however, that I have to state that this otherwise excellent and useful work
is full of errors regarding Irish locahties, — errors, too, of the strangest kind,
not mineralogical, but geographical, and which one would scarcely expect
to find made respecting the divisions of an Asiatic country. I do not speak
of such errors as Rovenagh and Borenagh for I3ovevagh (pp. 54 and SS),
Bum Beg for Bun Beg (p. 101), or Glen Maccness for Glenmacnass, which
are, however, too numerous to be pardonable, but of such errors as County
of Cavenagh for County of Caoan (p. 20) ; " Ballygahau mine, at Glandore,
County of Wicklow " (p. 27^), Glandore being in the County of Cork;
*' Knockniahou and Tigroney in Waterford " (p. .S0.5), Tigrouev being in
Wicklow; "In Wicklow, at Audley mine "(]>. ."ill ), Audley mine being
in the County of Cork. I hope a second edition will enable the authors,
not only to correct these errors, but to greatly extend the list of localities.
[ 338 ]
XLVII. On certain Inductions with respect to the Heat engen-
dered hij the possible Fall of a Meteor into the Sun ; and on a
mode of deducing the absolute Temperature of the Solar Surface
from Thermomefric Observation. Brj J. J. Waterston, EsqJ^
MR. CARRINGTON'S observation of the sun on the 1st of
Septembei* last having fortunately established the fact of
an outburst of light above the solar surface, and thus favouring
Newton's conjecture as to the sun receiving a supply of force
from bodies descending upon it, it may be worth while, and
perhaps assist in the formation of more exact ideas on the sub-
ject, if we compute, from Mr. Joule's value of the thermal unit,
the quantity of heat and intensity of temperature that would
accrue by a body falling into the sun or sun's atmosphere with
the velocity due to a parabolic trajectory. The modern inter-
pretation of Newton's conjecture is, that the comet, or by what-
ever name we call the body, does not supply fuel to a fire as oil
to a flame, but that it supplies force to the central radiating
energy — force to be converted into heat and light.
It is true that no body belonging to the solar system can fall
into the sun so long as the laws that keep them in their orbits
are maintained. A body that has once rounded the sun in a
parabola or elongated ellipse, will probably continue to do so,
unless in the rare case of the perihelion distance being so close
to the sun's surface that a slight perturbation from the other
bodies of the system may bring it within the limits of the sun's
radius. But when the orbit is a hyperbola, it is the first and
last appearance of the body ; and if, as may chance to happen,
the perihelion distance is less than the sun's radius, the sun must
inevitably absorb it. We are thus certain that the velocity of a
body that impinges on the sun must exceed 419 miles per second ;
for such is the orbital velocity in the parabola that separates the
lesser velocity in the ellipse from the greater velocity in the hy-
perbola.
With this velocity and Mr. Joule's unit it is easy to compute
the quantity of heat due to the conversion of the force ; and if
the absolute zero of temperature coincide with —461° F., the
zero of gaseous tension, the temperature attainable by a known
substance under such conditions may also be exactly computed,
independent of any theory or hypothesis whatever.
A pound of water falling through 772 feet acquires a velocity
of 222 feet per second, and a force that, if converted, raises the
temperature of the pound of water 1° F. If it falls through four
times 772, the velocity acquired is twice 222 feet, and the rise
of temperature 4°. Suppose the acquired velocity to be 1 mile
* From the Proceedings of the Astronomical Society for April 3, 1860.
Heat engendered hy the possible Fall of a Meteor into the Sun. 339'
per second, the corresponding rise of temperature is o64P, in-
creasing as the square of the velocity; and 419 miles per second
corresponds to 419 x 419 x 564 = 99,016,404°.
A pound of iron under the same circumstances would acquire
the same force ; but that force converted would raise its tempe-
rature nine times the above amount, because the same quantity
of heat has nine times greater effect in raising the temperature
of iron than it has on the same weight of water.
A pound of mercury would have its temperature affected about
thirty times the above amount, and so on according to the specific
heat of the substance.
Assuming that the specific heat of the body that impinges on
the sun is the same as glass, the rise of temperature correspond-
ing to the velocity 419 miles per second is 565 million degrees
Fahrenheit.
Thus the intensity of the temperature engendered depends on
the molecular constitution of the body : the quantity of the heat,
however, is independent of everything but the velocity and the
mass ; and each pound of any body whatever that strikes the sun
with the velocity 419 miles per second is endowed ^\nth force
sufficient to raise a pound of water 100,000,000 degrees of Fahr-
enheit's scale.
Has the mass of the sun been gradually collocated by matter
thus descending ? To estimate exactly the probability of this,
two other data are required, viz. the temperature of the sun^s
surface, and the quantity of heat radiating from it in a given
time. The first is unknown, but the second we know approxi-
mately from the observations of j\I. Pouillet, also from those of
Herschel and Forbes. It is estimated that it suffices to melt
a stratum of about 2 feet thickness of ice at the earth's mean
distance in twenty-four hours. This is equivalent to 1"04 foot
of ice per second at the sun's surface. Now it is known that
ice requires 142° F. to melt it, and each of those degrees is
equivalent to the work expended in raising the weight of the ice
772 feet against the force of gravity at the earth's surface. We
thus deduce that a weight equal to that of the ice arriving at the
sun with a velocity of 2649 feet, or half a mile per second (viz.
the velocity acquired in falling through 142 x 772 feet), is equi-
valent to the force emanating from the sun in one second. If
the same amount of force is brought to the sim by matter moving
at the minimum velocity of 419 miles per second, the mass of
this matter must be less than the mass of the ice, in the ratio of
1 to the square of twice 419. Such a mass is represented by a
sphere of 11-068 miles in diameter, of the density of water.
Supposing the sun to have the same density and specific heat
as water, and comparing its volume with that of the sphere of
340 Mr. J. J, Waterston on the Heat engendered by the
11 miles diameter, and allowing for the time, we find the
sun's annual loss of temperature to be 6^-125. This is a simple
arithmetical deduction from the fact that the sun's heat can melt
about 2 feet of ice daily. The observations of Herschel and
Forbes fix it at 1-835 foot (Phil. Trans. 1842); those of M.
Pouillet at about one-third less (Taylor's Scientific Memoirs,
vol. iv.). If we assume 1'5 foot as the correct thickness, the
yearly reduction of temperature is 4"'59. If the specific heat of
the matter of the sun corresponded with iron, this decrement of
temperature would have to be multiplied by 9, and so on for
other assumed values. But it is convenient to found our ideas
of such quantitative relations on water as the standard most
familiar.
Assuming the earth to have six times the density of water, we
may extend these calculations ; and comparing volumes and time,
we deduce 69 as the number of years that the sun takes to throw
out as much force as would accrue to it by the earth falhng down
upon its surface. The mechanical force thus supplied would be
equivalent to the expenditure of heat-force for 69 years ; and the
rise of temperature of the whole mass of the sun, supposing the
increment of heat uniformly diffused through its mass, would ap-
proach as much nearer to the maximum limit 317^ ( = 69 x 4"'59)
as the temperature of the planet after impact exceeded the tem-
perature of the sun.
Again, if we suppose the planet after it has struck the surface
of the sun to settle into a disc of 60,000 miles diameter, having
the temperature of 100,000,000 degi-ees, the temperature of the
sun being 12 millions, we should have oho^^ ^'^ ^^^ ^^^^ shining
with eightfold lustre, ginng out probably eight times as much
g 2 2
heat as an equal surface in the normal state. Thus = ^
represents the increment of solar heating power ; and if we esti-
mate the normal amount as what is requu'ed to keep the earth's
surface at a mean temperature of 60° F. or 521° absolute, we
521
see that -^y- = 17° nearly, is the increment of mean temperature
oi
over all the earth that would arise from such a planet-fall.
M. Pouillet infers from his observations on solar radiation,
that the temperature of the sun's surface is at least 2660° F.
If it do not exceed this amount, the rise of temperature in the
whole mass of the sun would be about 200'; but if, as before,
we assume the planet to settle into a disc 2' in diameter, we
have Y^iyth of the sun's disc shining with 38,000 times the normal
force, so that a planet-fall of this magnitude would increase the
radiating power of the sun 171 times.
possible Fall of a Meteor into the Sun. 341
Such extravagant conclusions only show the insufficiency of
our data^ and demonstrate the uncertainty in which the subject
is involved; so long as an approximation to the actual tempera-
ture of the solar surface is wanting.
Is it possible to ascertain the temperature of the radiating
surface of the sun ? Ordinary observations give us the tempera-
ture in the sun and in the shade. Suppose the temperature of
the sun to be double its present amount, it is probable that the
absolute temperature in the shade and in the sun would also be
double the present amount; consequently, also, the difference
between them. We might thus expect this difference, when due
precautions are taken, to be a constant quantity, and to be a
function of the sun's absolute temperature.
Suppose a thermometer to be enclosed in a vacuum and sur-
rounded on all sides by matter having a uniform absolute tem-
perature t : we may consider it to be the centre of a sphere, the
interior surface of which radiates heat to it, and the balance of
temperature to be thus maintained by reciprocal radiation, — as
much power issuing from the thermometer on all sides tow^ards
the concave surface of the enclosing sphere as enters into it by
radiation from the concave surface. There is a dynamic inter-
change of force in constant operation. If the temperature of
the sphere is augmented one degree, the thermometer rises until
its radiating power increases to the same amount. If half the
concave surface remains at /, while the other half increases from
t to / + 2°, the rise in the temperature will be the same as before,
viz. 1°, because the supply to it is the same as if the whole sur-
face were raised 1°. If -j-oVo^^ °^ ^^^ surface had the tempera-
ture / + 1000°, the other parts remaining at t, we have
lx(/ + 1000^) + 999x^_ o
1000 -^+1,
the resulting temperature as before. If yy'o^^^ ^^ *^^ surface
had the temperature oi t + 2000°, then
Ix (^ + 2000^) +999 x/_ o
1000 ~ '^^
is the temperature of the thermometer ; and generally, if - of
the surface of the sphere had the temperature t-{-x°, we have
(< + ^°) + (n-lV ,
n = ^ + '''
the temperature of the thermometer. Hence x'^^=-nr'^, a simple
relation, by which we can deduce the temperature of the sun's
radiating surface, assuming for the present the non-absorption
Phil. Mag. S. 4. Vol. 19. No. 128. May 18G0. 2 A
843 On the Heat engendered by the Fall of a Meteor into the Sun,
of rays in passing through the atmosphere. It will be remarked
that T° is the diflference of reading between thermometers in the
sun and in the shade taken with due precautions.
Some years ago, when in India, I tried this by enclosing a
thermometer within three concentric boxes well protected from
external inHuences, and capable of being equally heated all round
to any temperatui-e below 400°, by means of flues ascending
from an Argand lamp. The sun's rays, when near the meridian
(having an altitude of about 70° and \\ith the atmosphere per-
fectly clear and calm), were admitted to fall, when required, on
the bulb of the thermometer through a narrow triplet glass par-
tition, I found that 50° was the rise that took place in conse-
quence of exposure. There being glass partitions on both sides,
the reading of the thermometer was very distinct by transmitted
light. Beginning at 80°, without applying the lamp, the ad-
mission of the sun's rays caused the mercury to rise to 130°,
where it remained steady. The lamp was then applied at low
power, so as to maintain the inner box at this temperature while
the sun was excluded. "When perfectly steady, the suu's rays
were readmitted, and the mercury again mounted with the same
alacrity as before, until it reached 180°. This continued step
by step up to 250°. No difference, either in the magnitude of
the step or the time taken to effect it, could be detected.
Thus, for T° we have the constant 50°, and n we obtain by
comparing the disc of the sun with the surface of the sphere.
At the earth's mean distance the sun's diameter is 32' 3"'6,
lience n= 183960 and a; = 918000°.
If there is no fault in this mode of proceeding, we may with
confidence estimate the solar temperature to he above 10,000,000
degrees, probably 12,000,000, allowing a reduction of one-third
from absorption in passing through the atmosphere and the
three plates of glass.
A notable fact, in making these observations, is that the step
T° seems wholly independent of the temperature of the medium
in which the thermometer lies. AVhy this should be, is apparent
from the equation. Substituting 2t for /, and consequently
X — ^ in place o{ x, is tantamount to heating the box from 80°
up to 620°. Let t' represent (in degrees) the step at this higher
temperature 2t, we have
n T X
Thus the step diminishes only about the y^o uth part, or V^uth
of a degree during a change of upwards of 500° in the box.
From Mr. Carrington's observations it appears that the burst
of light was of much greater intensity than the sun's normal
Controversy between Archdeacon Pratt and Prof. Haughton. 348
surface. This is quite consistent with its assumed temperatui'e,
which is much less than any probable estimate we can make of
the temperature of the conversion of the force of a body striking
the sun's atmosphere with a velocity of from 400 to 500 miles
per second. The existence of a transparent atmosphere seems
also to be positively demonstrated by the blaze occurring above
the spots.
Edinburgh, February 15, 1860.
XL VIII. Controversy betiveen Archdeacon Pratt a7id Professor
H aught on.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen^
IN Archdeacon Pratt's last paper, published in youi* Number
for the present month, he states that the question at issue
between him and Professor Haughton is not what I have repre-
sented it to be, namely, by what rule the equation
^Cin I C" .d.a'^e' a'^C^de' ma^ L- , ,, ^ ^^^^
is to be differentiated when the continuity of the laws of the
density and the ellipticity throughout the entire mass is not
assumed. Professor Haughton asserts that, by the process of
differentiation, and without the assumption, he can deduce the
equation
fe 2p^ de^_6e/ po^ \
da'^^ya'^da aA^ 3j>W~ ' ' * ' ^^^^
from that just given. Ai'chdeacon Pratt asserts that, without
this assumption, the second of these equations does not follow
from the first. If this be not a controversy as to the proper
mode of differentiating equation (12), I confess myself quite
unable to understand what it is. IBut to obviate all possibility
of misconception, I assert, and shall proceed to prove, that
equation (13) does follow from equation (12), without any
assumption as to the law of density or ellipticity for the solid
part of the earth.
I will suppose that, for all values of a! from a' = 0 to a' = a (in
other words, for the whole of the fluid nucleus), we have e'=(f){a'),
p'z=-^{a'), and that, for values beyond a, we have t^=f{a'),
p' = F(rt'),/ and F denoting any functions, continuous or dis-
continuous,
2 A2
344 Controversi/ between Archdeacon Pratt and Prof. Haughton.
Let M be the entire mass of the earth. Then since
M = 47rj pa",
Jo
if we introduce this value into the last term of equation (12),
multiply by a^, and substitute for e' and p' their values, we shall
have
«V(a) J>^(«')-gJV(a') '^-"^-J^W) •/'(«')
This equation applies to the surface of the fluid nucleus. For
the next surface de niveau within the fluid the equation will be
{a-hy
-8^(''-*)==0.
Expanding and retaining terms of the first order only, we find
-{2««^(«)+«Y(«)} fW(«')-«Y(«)^(«)+ ^^fl^^^^^
+ a^y F(«')/(«') - g a^^[aW[a) + ^^ =0 ;
or striking out the terms which cancel each other, and dividing
* If I rightly understand Archdeacon Pratt's reasoning, he supposes
that, under the conditions stated in the text, the differential coefficient of an
expression such as
Jo Ja
with regard to a would be
my\r{a) — JiF(a).
This, however, is not so. It is easily seen by the mode of reasoning
adopted in the text, that this coefficient will be either
{m—n)-^{a) or (m— n)F(a),
according to the region to which we suppose the differentiation to apply.
The result,
7n-^{a) — nF(a),
could only be obtained by the substitution of a— A for fl in the first inte-
gral, and of a + A for a va. the second, a process which would be of course
illogical.
')
Mr. Woolhonse on the Deposit of Submarine Cables. 345
«y 0 » 1
This equation also holds for the surface of separation. For
the next surface de niveau within the fluid it becomes
Expanding as before, and arranging, we find
which is identical with equation (13).
The foregoing investigation is of course only an application to
the equation (12) of the principles which I stated more generally
in your Number for December. I regret that Archdeacon Pratt
has obliged me to occupy your pages with a second discussion of
a question which in fact belongs to the elements of the integral
calculus.
I am. Gentlemen,
Your obedient Servant,
Trinity College, Dubliu, John H. Jellett.
April 1860.
XLIX. On tJie Deposit of Submarine Cables.
ByW. S. B.WooLHousE, KR.A.S., F.S.S. ^c
To the Editors of the Philosophical Magazine and Journal,
Gentlemen,
MY attention has recently been drawn to the dynamical
theory of the submergence of telegraphic cables, which
has already been discussed both theoretically and practicall}^, at
some length and with considerable skill, by Messrs. J. A Long-
ridge and C. H. Brooks, in a valuable paper read before the
Institution of Civil Engineers, Feb. 16, 1858. The mathema-
tical theory originally laid down in this excellent paper has since
been established, by a different form of process, in an elegant
paper by Mr. G. B. Airy, the Astronomer Royal, inserted in
your valuable Journal for July 1858. Independently of the
practical importance of the subject as an engineering operation,
the investigation of tlie several relations appertaining to it is not
devoid of mathematical interest. Indeed I have found the in-
quiry to be so inviting as to lead me not only to simplify, but
to extend the investigations of the general problem somewhat
346 Mr. Woolhouse on the Deposit of Submarine Cables.
further than is contained in these papers ; and having, moreover,
considered the subject in its more practical bearings, it is pre-
sumed that the contribution I am now about to make may be
considered of sufficient value for publication.
To avoid confusion we shall, as far as may be practicable,
retain the notation and general arrangement of the Astronomer
Royal, and for present convenience we shall here briefly state
the principal symbols employed, viz. —
n the ship's velocity.
m the velocity of delivery of the cable.
X the horizontal ordinate of a point in the cable curve, mea-
sured, from the point where the curve touches the ground,
in the direction of the ship's motion.
x' the same, measured from a fixed origin.
7/ the vertical ordinate of the same point, measured upwards
from the bottom.
s the corresponding length of the curve.
0) the inclination of the curve with a horizontal line at the
same point.
p the radius of curvature.
T the tension, as measured by the length T of cable weighed
in water.
g ( = 32*19 feet) the accelerative force of gravity in one
second.
' g' the same when diminished in the proportion of the cable's
real weight to its apparent weight in water.
m
a = —J twice the height due to the velocity m with diminished
gravity.
I. ^Ye have first to discuss the problem on the hypothesis
that the resistance and friction encountered in passing through
the water shall each vary simply as the velocity.
The bottom of the sea is also supposed to be level, and the
cable perfectly flexible.
Assume ^ ^jjg coefficient of lateral resistance,
b' that of longitudinal friction,
_ bn lateral resistance to velocity n
g' diminished gravity
Then, with respect to an element 8s of the cable, we shall have
Normal velocity . = n sin <y "1 , ,
rr, . 1 / . >downwards,
langential velocity =m — /icoswj
Normal resistance = bn sin to "I -,
m • -, n ■ ■ 1, , ^ >upwaras.
langential rriction =b' [m — ncoswjj
Also if the tension were measured by the real weight of a length
Mr. Woolhouse on the Deposit of Submarine Cables. 347
of cable, we should have that length = ^ T. Therefore for the
accelerative forces on the element hs due to the change of tension,
we have
Horizontal force =g ^( - T cos w j =9'-f (T cos w),
Vertical force =^ k- ( - T sin w j =y ^ (T sin co) .
By resolving the resistance and friction, the total impressed
accelerative forces are therefore, —
Horizontal = ^ -7- (T cos &>) —bn sin^ <u + 6'(m— n cos &>) cos ©,
Vertical — 9^ -j (Tsinw) -^ +5wsin&)C0sa)+Z>'(m— ncos&))sinei>.
Now if we suppose the movement of the cable to be steady,
so that it shall be uniformly deposited at the same speed at
which it is delivered, and such that the suspended portion shall
retain its form, the absolute velocity of a definite point of the
cable will evidently result from a movement down the curve at
the velocity of delivery taken in combination with an onward
movement of translation equal to the ship's velocity. Thus we
have
ds da^ d'^x' dcosa> „c?cos&>
Jt^"^' ^=n-mcosa,, ^ = -m_^^ = m^— ,
dy . dhi «?sinft) oC^sineu
It may be proper to observe that these conditions of steady
movement, on which the investigation is made to depend, can
only be accurate when the cable is paid out at the same speed as
the ship's velocity, or when m=.n. When this is the case, it is
evident that, whatever may be the initial disturbances, the move-
ment will soon cause the cable to assume the permanence of form
here supposed. The conditions will, however, approximately
subsist when m differs but slightly from n, as the form of the
curve will then only be subject to a very gradual change. But
if m should differ much from n, we ought not to place much
reliance in the accuracy of the results*.
rf^y dhi
Equating the values of -r-^, ^^ with the impressed forces,
* The discussion of the jiroblem, taken in all its generality, supposing
the form as well as the position of the curve to vary, would load to ex{)rcs-
sions tpo complicated to be of any ])ractical utility- Besides, this is not
needed, as all irregular movement should be avoided during the operation.
348 Mr. Woolhouse on the Deposit of Submarine Cables.
we have
in'
m
2</C0S0> / C? /m \ 1 • o 111 \
— -J — '^9 ~j~ \\ cos a>) — on %\\\^ on + b'[m — n cos &>) cos to,
ds ^ ds
, rfsino) id ,m ■ s II- II, s •
= g ~r [L^xnoo) — g' -\- onii\\\(oco^(i} + b\m — ncosa»)sm&>;
cos 0)
ds ^ ds
or, after transposing and dividing by g\
0=^{(T — g)cos(u}— esin^ &)+ j-( cosw j
0= -r{\^ — fljsinft)} — l+esin&>coscB4--Te I cosw )
Multiply these respectively by cos w, sin &>, and add j and next
multiply them by sin to, cos on, and subtract ; then
dT
(1)
smo)
b' (m \^
—J- = sma> — rcl cos co I
ds 0 \n /I
.r^ .d(o
(i— c) -y-= cosct)— esm &>
The latter of these equations gives
T— a=/3 (coso)— esino)) ;
and at the lowest point where &) = 0, Tq— a = pQ.
From the equations (2) we also obtain
(2)
(3)
</T
= d(o
b' (m \
> — T e\— — coso) j
b \n J
_^_ . ... (4)
T — a '""' coso) — esincD
To integrate this equation, put e= cotX ; then A, is evidently the
limiting angle or maximum value of w, and
sin (A,— &))
cosw — esm &) = ■ — -f— - — ,
smX,
sincD=sin Xcos ^ — w) — cos \ sin (X,— &)),
cos &>= cosXcos (X — <w) + sin X sin (X — o)).
Substituting these values in (4) and integrating, remembering
that T — fl = po when ft) = 0, we get
T— a -2^1 ^"^'^
log = sm-* A-loff—
• 0) cos X sin X
/3o ""Sin (X— oj)
V \ ^ • , 1 sinX . „^ m . _ ,
+ y ei cos XsniX log ^3777:^ ^+a)sm''X smXlog
V
= ( sin^ ''^ + "T cos^ X ) lo
.inx(l-|)
sm (X— (w)
sinX
tan^^X
tan|(X— 0))
an ^ X ■»
tan ^X
sm^X+ "tCOs^X llog-. — -^ ^^ 1 — cos X log ^ , ,^
b / ^sm(X— ft)) bn °tani(X— <u)
— (BCOsXsm
(5)
Mr. Woolhouse on the Deposit of Submarine Cables. 349
Again, substituting the value of T — a given by (3), we get
log^ = U~ (l- ^) cos'x) log ,^i^
Po L \ 0/ J °sin(A,— co)
b' m ^ , tan ^ X / , b'\
-^-eosXlog^^^,^^_^p(^l-^ja>eosXsmX, . (6)
which is an equation of the cable curve, determining the propor-
tionate radius of curvature in terms of the angle w.
Also since
— = !—«?&>, — = 1 — </&) cos w, —= \—d(o sine),
Po JPo Po JPo Po J Po
these are functions of co alone ; and the constant Pq, on which
the absolute magnitudes depend, may be found by comparing a
J/
calculated value of -^ with the known depth of the sea.
By integrating the first of equations (2) we have likewise the
following relation,
(7)
T-a=p,^-y-^e[^-s^xy
z-
The foregoing equations, which are general, become much
simplified if we assume, as Mr. Airy has done, that 6'= 6 and
m=;i. Thus if we put
/ tanjX \-cos\
ltani(X-(y)J ' • • • • (»j
the values of which are evidently comprised between 0 and 1,
equation (5) gives
T— a _ sin\
■"^~sin(X-&))'"^ (^)
and equation (7) becomes
T-a = pQ-\-y-e{s-x) (10)
Equations (1) also become
0= j-{{^—a) coso)}— <?(1 — coso)),
0= ^-{(T— fl) sin &)} — l + csinw,
and, by immediate integration, give
(Y -a) cos CO =pQ-\-e{s-x)'\^ _ ^ /jjv
(T— a) sinaj = 5 — ey J * ' * * v /
350 Mr. "Woolhouse on the Deposit of Submarine Cables.
The first of these and (10) give
(T-G)(l + eosft)) = 2/Jo + y 1
(T— fl)(l - cos to) = y-2e(s-a;) J '
(12)
And from (9), (11) we deduce
T-fl sin(\-(u) T-a
Po
sin\
y
Po
(coso) — esintw)
(13)
= l-e— +e^^.
Po Po
The coordinates and length of the curve, as compared with Pq,
the radius of curvature at the lowest point, arc hence determined
by the simple formulae
tan i (X— w) = tan i X . z^^'' \ '
T — a sinX
Pq sin(X— &))* '
-^ = (1 + cos (o) —2,
Po Po
Po Po ^ '
s y T-a .
— =e-^H sm«.
Po Po Po
The Tables given by the Astronomer Royal can be constructed
with the greatest possible facility from these formulae ; and if
the first of them be replaced by equation (8), the calculations
may be performed for given values of co.
For any integral value of e, up to 10, the constants may be
taken from the following Table : —
e.
X.
cosX.
secX.
log tan i X.
log sin X.
1
45 6-0
0-70711
1-41420
9-61722
9-84949
2
26 33-9
0-89444
111802
9-37303
9-65052
3
18 261
0-94868
1-05410
9-21026
9-50000
4
14 2-2
0-97015
103077
909027
9-38478
5
11 18-6
0-98057
101981
8-99572
9-29251
6
9 277
0-98639
1-01379
8-91783
9-21590
7
8 7-8
0-98994
1-01016
8-85167
9-15051
8
7 7-5
0-99227
1-00779
8-79419
909354
9
6 20-4
0-99389
1-00614
8-74340
9-04309
10
5 42-6
0-99504
100499
8-69789
8-99784
At any time during the actual operation of laying the cable,
it is evident that the ship's velocity, the depth of the sea, and
the tension and inclination of the cable at the ship, can be ascer-
tained by observation. With deep water the inclination w will
Mr. Woolhouse on the Deposit of Submarine Cables. 351
not differ much from the limiting angle X ; and as a small error
in (o would then considerably affect the other values, it will be
preferable to determine this angle by calculation. For this pur-
pose we have
=^=l + cosa>-2 ^— — -M -^ wf— S r • • (14)
If for given values of e or \, values of this expression be calcu-
lated and tabulated under co, then by entering this Table with
the known values of „-,_ , the angles to will be readily deduced.
From (12)j
X 9 1 y — 2e(s—x)
tan® |CJ= ^ -4r ' ;
. 9. _y-2e{s-x)
"^P^- tan^o, -^'
Hence we conclude that when, by extra paying out, the amount
of "slack" or "stray length" (s— a?) is increased, and the in-
clination o) also increased, the radius (po) of curvature at the
lowest point of the curve becomes sensibly diminished; and it
will be evanescent when
2e = 1 — tan^iftj.
y "•
The value of ihe constant p^ will perhaps be best determined by
the formula
^^^(T-a)(l + cos.)-y^ . . . (15)
and the amount of stray length by the formula
s—x= C'^~^)cosft>-po
e
_y — (T — «)(! — coso))
~ ScotX '
(16)
which are deduced from (11) and (13). For the calculation of
these the observed value of w will probably be suflSciently
accurate.
We have only further to remark that the curve has a recti-
linear asymptote inclined at the limiting angle X with the hori-
zontal ; that the horizontal distance of this asymptote from the
lowest point = ^, and the horizontal distance from any other
point of the curve = this distance multiplied by ~. Also if
from any point in the curve a tangent be drawn terminating in
352 Mr. Woolhouse on the Deposit of Submarine Cables.
the asymptote, e times the length of this tangent will be equal
to T-c.
II. ^Ve propose now to renew the investigation, assuming the
resistance and friction to each vary as the square of the velocity,
which supposition is more nearly in accordance with the actual
resistances as determined by experiment. Let
B be the coefficient of lateral resistance,
B' that of longitudinal friction,
2 _ Bn^ _ lateral resistance to velocity n
g' diminished gravity
Then with respect to an element hs of the cable^ we shall have
Normal resistance = Bn^ sin^ w,
Tangential friction = B'(m — wcostu)^;
and, proceeding as before, we obtain
m^ — -J — =^'^(Tcos&)) — B/i'^sin^o) +B'(m — ncosa))^cos6),
m^ — -^ — =y y(Tsin6))— y + Bn^sin^o)Cos&) + B'(m— ncos&))^sina);
or, transposing and dividing by g',
0=-3-((T— fl)cos6t)} — e^sin^w + t^e^f cosw j coso),
0 = -j-{(T— o)sin&)} — 1 +e^sin^6JC0s&) + ^e^( cosw j sincu,
which, in substance, are the equations finally arrived at by
Mr. Airy.
Multiply equations (1) respectively by coso), sinew, and add;
and aftem'ards multiply them by sin w, cos &), and subtract ;
then
dT . B' Jm \n
-^- = sinw— r=^ e-^l coscy)
ds B \7i / 1 ,^.
(T — c) -7- = cos w — e-sin^&),
which agree with the equations obtained by Messrs. Longridge
and Brooks*.
* In the investigation of Problem III., Messrs. Longridge and Brooks
have disregarded the effective forces as inconsiderable. To supply these,
we have, at the point C, the horizontal velocity =i'( 1 — cos »), and the ver-
tical velocity ^ — i/sint*. Now with any variable velocity V, the effective
accelerative force =-.-=— i' —— ; and multiplying by —.ds and in-
dt as g
(1)
dT '^"^
Mr. Woolhouse on the Deposit of Submarine Cables. 353
From the latter of these equations,
T — a=/3 (coso) — e^sin^o)) ; .... (3)
and at the lowest point where &)=0, Tq— a=po« Equations (2)
also give by division,
o>— i^e^i coso) I
m ="<y 9-^-2 . ... (4)
i — a cos &) — e^ sinr oi ^ '
To facihtate the integration of this expression, let X be the
limiting angle of the curve or value of w which makes
cos CO — e^ sin^ o) = 0.
Then
0= cos \—e^ sin^ \ = eS cos^ X.+ cosX— e^ ;
and if for brevity we put cos X = a, « and will be the roots
a
of the quadratic,
«2+^-l=0 (5)
Therefore
1 1
coso) — e*sin*&j
^ (cosct)— «)( cos &) + - )
_ l-aV ^ 1 \
"~ 1 +a^\COS CO — a 1/'
+ 1.
COS O) + •
a
By substitution and integration,
1
_, 2 cosa) + -
^"s-7-=r+a-^^°^c-^i^;r::-u
(m \2 /m Y
( cos a> I I cos o) J
B' g f
cos CO — a 1
cos CO H —
>•.
a
tegrating, the accumulated force, as measured by weight in water, = jV.
Therefore the vertical effective force =-T sin A, and the horizontal force
^2 9
=——f (1— cosA). If the expressions (1) and (2), instead of being put
g
equal to zero, be respectively equated with these, the only eflFect on the
equations (3), (4) which result from them, will be the substitution of t j
for t in the latter, and they are then identical with our equations (2).
The correction — r-, or a, is always a very small quantity.
9
354 Mr. "Woolliouse on ike Deposit of Submarine Cables.
But
/m \2 /^ Y
[--coscoj \,[n-V
= cos co—\ a J H ;
COS&)— a \n / coso) — a
j- =oosa,-(^- + -) + J ,
coscoH — coswH —
a. a.
1
„ 2 cosaj+-
1 1 — a 1 — a^ 1 a
C i+a-^ ^ COS &) — «
B l-t-«2 ' a cosw — a 1
•- I COSW +
a
whichj fiually integrated and corrected so as to make Tq— «=/3o
when £0 = 0, gives
1 T — a _1 — «^i /I— « acos&) + l\
iog-^_^_— ^log^^^-^.— ^^_^ ;
_ j^X^Q-L ^^ ^ ipcr 1 — acosw + sino) -v/l — a^
g.^_isina>v/l-a2
(1 4- a^) V'l — «^ a COS 0) +
^'}-(«)
If the value of T — a by (3) be substituted, we shall obtain an
equation of the curve exhibiting the radius of curvature at any
point as a function of co.
To adapt the expressions to numerical calculation, assume
2e^=tan2/i, cosX=tan/Xj cosa) = tan^; . . (7)
then
- + a = 2 cosec 2/x, a=2cot2u, 5 = cos2ii,
Therefore
Mr. Woolhouse on the Deposit of Submarine Cables. 355
1 — a acos <» + 1 _ , 2 1 Tk ^^^ 1^ ^^^ ^ ''" ^ _ ^^^^ i^
1+a cos CD — a ^ tan^ — tan/j, tan (^ — /j,)'
1— fltcosco + sintoV'l— «^ _ 1 — cos (X + a>)
cosftj— « cos ft)— cos X
2sin^^(X + 6>) sin^(X + <a)
~ 3 sin^(A- + co) siu^ (A,— «) "~ siii-^(X,— w)*
smtuV'l— a^ ,1 , cos«D + a
Affain, if sin olrrr: ; then cos -v|f = r, and
° ^ «cos<« + l a cos 6) + !
, 3, , 1 — cos -xlr (1— a)(l — cosw) ^ o,- , 2 1
tan* i>|r = .i — y = TT-j — fh-; ( = tan^ f \ tan^ ict>.
^^ l + COST^ (l+a)(l + COSO)) ^ ^
Hence
, T-a ^ , tanH^- B'f cosVM X''
log__= cos2/.log^^^^^-^^ - 53 1^0-:^^ (^--«j
sini(X + a>) _ 2sin^/m 1 V^^^., i;, tanico)|.
^sin^(X-o)) sm\\n a/ ^ ^ ^ 'j
Or, if
"" =cos2/i, c2=T-x-=tan2i\, 03= log e x arc of 1°,
c,=
1— 1 j^«2
l+a2-— r-^ -2 l + «
"W "/ cos^/i/m \2 /l — a ^ ,^
\ ra / _ cos''/*/. m y
"6 -3(1 + ^2)
then
, T-« , C2 B' r , , sin|(\ + 6))
log = C. log 7 77j X — tT 1 %<^ + ^4^00 "^ TTT \
^ Po ^ ^tan(^— /a) B L °sm^(X-a))
— C6tan->(c5taniG))\ (8)
in which (o is expressed in degrees, and the logarithms are now
adapted to the system of Briggs as commonly used.
The logarithmic values of the constants, including the angle
fjL and the limiting angle \, are given in the following Table for
integral values of e, and supposing that m = n*.
* When the ship is stationary, or e=0, the curve is the commou cate-
T-a T— o
uary, and X=90°, «=0; .".by (fi) = sec a, and by (3) -■ =co»(»;
Po P
356 Mr. Woolhouse on the Deposit of Submarine Cables.
log C3= 7-87966.
e.
X.
M-
logCj.
log c..
log 04.
log<?s-
log c,.
0
90 d-0
6 00
000000
000000
— 30
0-00000
8-18069
1
51 49-6
31 430
9-65052
9-37304
8-91908
9-68652
8-56267
2
28 13
41 26-2
909355
879424
816171
9-39712
8-80811
3
18 55-2
43 24-6
8-7440()
8-44348
7-65260
9-22174
8-97051
4
14 150
44 G-3
8-4!)4t34
8-19382
7-28361
9-09691
9-09040
5
11 250
44 25-6
8-30U94
7-99965
6-99514
8-99983
9-18513
6
9 310
44 361
814203
7-84067
6-75820
8-92034
9-26335
7
8 110
44 42-5
8-OOS 75
7-70903
6-56034
8-85452
9-32837
8
7 90
44 46-6
7-89278
7-59143
6-38534
8-79572
9-38670
9
6 21 5
44 49-4
7-79047
7-48928
6-23266
8-74464
9-43738
10
5 430
1
44 51-4
7-69896
7-39670
609583
8-69835
9-48342
m
For brevity put k =. and
Po
i_C dco sin 0) _^~^^i /I — « acosaj+l\
~J cos(u — e^sin^fu 1+a^ °\l+a cosoj—aJ
or
tan {d-[i,y
tan {6—fi):
■Cc,€
2^ '. (9)
Then employing h as an independent auxiliary variable, we shall
have
1 ds _ p d(o _ p cos 6) — e^ sin^ oi _ T — a _ k
Po ^^ Po ^^ Po ^^^ ^ Po ^^^ ^ ^^^ ^ '
Hence by assuming a uniform succession of values of h and
calculating values of 6 from (9), and thence values of <o from (7)
and k from (8), the corresponding values of — = ^kdh can be
obtained by the method of quadratures. Thus, if the values of
k be differenced twice, and {k) denote the arithmetical mean
Po
= sec*w. Hence also in this case.
— = \- — = \ da sec-a)=tanoj.
Po ^ Po *^
— = i^— ^COS(j)=: \(ia)sec<a = logtan(45°-}-5ca).
Po " Po '^
V Co dill c I ^ 1
-^=1 \ ^ — =: \ (1(0 seCG>tanci)=: sec co — 1.
Mr. "Woolhouse on the Deposit of Submarine Cables. 357
of two consecutive values k, k + Ak, and (Ag) the mean of the
second differences which stand respectively opposite to them,
the increment of — may be calculated from the formula
Po
^(£)=w-g(^''-
>Po
For the computation of — we have
Po
\ djc 1 ds J ^
• -77 = • —r cos 0} = k cot CO ;
Pq ah Pq ah
but as the value of this quantity is indefinitely great when co is
indefinitely small, the integration by the same method becomes
impracticable. To obviate this inconvenience, calculate a table
of the values of
„ 1 du; -
'4= 77 vh = k V h cot CO,
Po dh >
X
which will not be subject to anv abrupt change. Then — will be
dh " P^
the integral of Q — -=.
vh
The value of Q at the lowest point of the curve, where g) = 0
and h = i), may be found thus: — Since kQ=^\, we shall have in
the immediate vicinity of this point -^=.idh=^h. Also since
an element of the curve will coincide with the circle of curvature,
we shall also have x=^ ^^y{.^Po~!/) > ^^' substituting y = pQh,
X , 1 dx - /l —h , ,_
Now the quantities Q being differenced, and A,, A^, kc. de-
noting the differences which immediately succeed a given value
of h, and representing the values of h by ordinal numbers q, so
that q= -r-r, the value of Q when h becomes h + iS.h, or when q
becomes q + i, will be Q-}-/A,+ — .^ — A., + &c. ; and the in-
X ^
crement of — in passing from h to /^-f- A//, or from q to q + l,
Po
will be
.X , f» di r^ .. i{i—l). , 1*
A--= y/M\ ~^--=-A q+jA, + ^^A2, &c. y .
Po Jo v</ + i L •^ J
* For the integration of the terms of tbis expression I Inve arrived at
the foUowin}^ curions general form : —
Phil. Mai;. S. 4. A^ol. 19. No. 1.28. May 18G0. 2 B
358 Mr. "Woolhouse on the Deposit of Submarine Cables.
Also, if for brevity
Jo v/^ + » Jo x/q + i
di
r
di
x/
J-
q + t
.i^=(2).
=. t
3_
(3), &c.,
'0 "/q + i
the values of these integrals may be deduced from the formulae
(0)=2{v/gTl-^^},
{l)=§{^^T+l-q{0)},
i^) = H^q+l-2q{l)},
(3) = f(v/^_35(2)},
&c. &c.
Hence the coefficients of Q, A„ Ag, &c. in the value of A —
Po
may be found with the use of a Table of square roots. Those
of the first two will be sufficient for our present purpose, pro-
vided that A, be diminished in each case by one-sixth of the
mean value of Ag; and the values up to 5 = 30 are exhibited in
the following Table : —
Coefficients for integrating Q-— p=.
V a
Coeflf, of
Coeff. of
Coeflf. of
Coeflf. of
7-
Q.
^l-i(^2)-
9-
Q.
A, -K^,).
0
200000
0-6667
16
0-24621
0-1225
1
0-82843
0-3905
17
0-23907
01190
2
0-63567
0-3071
18
0-23252
0-1157
.3
0-53590
0-2615
19
0-22647
0-1128
4
0-47214
0 2317
20
0 22088
0-1100
5
0-42684
02102
21
0-21568
0-1074
6
0-39252
0-1937
22
0-21083
0-1050
7
0-36535
01«06
23
0-20630
0-1028
8
0-34315
0-1699
24
0-202(;4
01007
9
032456
0-1609
25
0-19804
0-0987
10
0-30869
01531
26
0-19427
0-0968
11
0-29495
0-1464
27
0-19070
0-0951
12
0-28290
0-1405
28
0-18732
0-0934
13
0-27221
0-1353
29
018412
0-0918
14
0-26265
0-130.)
30
018108
00903
15
0-25403
0-1263
The value of the integral might be otherwise found by putting
it under the form 2j QJ(v^A), and considering \^/i as the auxi-
liary variable.
If we examine the foregoing equations, it will appear that
the longitudinal friction which introduces the terms containing
Mr. Woolhouse on the Deposit of Submarine Cables. 359
B', has so little influence on the/orw of the curve that its effects
may be practically disregarded, and their omission will greatly
simplify the formula;. The differential equation (4), from which
we have obtained the formula (8) for determining the tension,
obviously indicates, when m. = n, that by neglecting the longitu-
dinal friction the value of the tension will be sensibly increased
only towards the upper extremity of the cable, and even there
but slightly, as the coefficient B' is small as compared with B.
Therefore by (3) the radii of curvature towards this extremity
will also be slightly increased in the same proportion. But as
this portiou uf the curve is nearly straight, it is evident that a
small proportionate augmentation of the large radii of curvature
cannot produce any sensible divergence throughout the limited
extent of the curve we have under consideration. For a given
value of 0) the coordinates x=z (*p dco cos a>, y = \p dco sin cc will
be both slightly increased ; but the point may be considered to
be merely transferred along the curve, as the divergence towards
the convex side will be extremely minute. AVe shall therefore
deduce the formulae assuming B' = 0, which will be more conve-
nient, and sufficiently accurate for all practical purposes.
Making B' = 0 in (6), we get
T— g _/]—«« cos ft> + l\i^_/ tan^^/j, ^ <=««2^
Po ""Vl + a cosw — a / ~ \ian {6 — fj-) J ' ^ '
Hence if Tj, w, denote values referring to ujuj given point, we
shall have
T — g _/«cosa)+l cos6)i — «\lzg_/cot(^— /i) \'''
Tj — a \acos&)j + l coso) — a/ \cot(^,— ^)j ' '
Again, since cos to — e^ sin- &) = e^ (cos aj — «)( cos &)+ -), from
(3) we get
T — a _ p COSQ) — a a cos 0)4-1
T, — a Pj cosWj — a acoswj + l*
p /cosoj — a\ ?_/acosft) + l\ ^
p, Vcosft),— a/ \acosa)j+i/ ' • \ J
Also the first of the equations (2) gives, by integration,
T-« = po + 7/; (13)
y /I — a a cos o) + 1 \ L^lfL ,
.-. — = (t- ^)' + «^-l, . . . 14)
Po \i + a costu — a/ ^ '
which is the equation of the curve. Or, adopting the former
constants,
^-\tan>-^)/-^ (^5)
2 B2
3G0 Ml*. Woolhouse on the Deposit of Submarine Cables,
tV s .
The values of — . — , if required, must be found, as before, by
Po PQ
the method of quadratures. As an example, I have taken the
case of e = 2, B'=^ B, Po=^y ^"^ carefully calculated the coor-
dinates, &c. from the general formulae; and the results are given
in the following Table: —
Table for
6 = 2, B' =
= iB,po
= 1.
r\ dx 1 —
k^^
h.
?•
(1).
dh
= T-a.
X.
y-
•00
0
0 00
0^70711
rooooo
000000
000000
•01
1
7 55 0
0-72557
1-01004
0-14205
0-01005
•02
2
10 58-3
0-74418
1-02021
0-20349
0-02020
•03
3
13 9^7
0-76294
1-03043
0-25137
0-03045
•04
4
14 540
0-78230
1-04076
0-29276
0-04081
•05
5
16 19-7
0-80227
1-05111
0-33016
0-05127
•06
6
17 32-5
0-82270
1-06165
0-36483
0-06183
•07
7
18 350
0-84376
1-07224
0-39753
0-07250
•08
8
19 29-7
0-86531
1-08288
0-42874
0-08328
•09
9
20 17-8
0-88712
109365
0-45880
009416
•10
10
21 0-4
090944
1-10451
0-48795
0-10515
•11
11
21 38-4
0-93237
111548
0-51637
0-11625
•12
12
22 126
0-95578
1 12655
0-54421
0-12746
•13
13
22 430
0-97967
M3771
0-57158
0-13878
•14
14
23 10-7
1-00408
1-14897
0-59858
0-15021
•15
15
23 356
1 •02891
1-16027
0-62528
0-16176
•16
16
23 58^0
1-05437
M7174
0-65174 i 0-173421
■17
17
24 18-3
1-08029
1-18329
0-67802
0-18520
•18
18
24 37-2
1-10649
1 -19495
0-70416
0-19709
•19
19
24 540
1-13316
1-20670
0-73020
020910
•20
20
25 9 3
1-16038
1-21862
0-75617
0-22123
•21
21
25 23-5
1-18801;
r-23058
0-78210
0-23348
•22
22
25 36-3
1-21607
1-24265
0-80802
0-24585
•23
23
25 48-2
1-24477
1-25490
0-8331)6
0-25833
•24
24
25 58-7
1-27397
1-26721
085994
0-27094
•25
25
26 8-7
1-30341
1-27902
0-88598
0-28367
•26
26
26 17-7
1 -33343
1-29217
0-91209
0-29653
•27
27
26 260
1 -36392
1-30482
0-93829
0-30951
•28
28
26 33^7
1-39483
1-31762
0-96459
0-32262
•29
29
26 40-7
1-42617
1-33052
0-99101
0-33586
•30
30
X =
26 47-0
28 1-3
1-45801
1-34360
1-01756
0-34923
The curve thus calculated will be a type for ail the forms which
can arise when (? = 2, as they will only differ as regards the scale
of measurement *.
"When B' = 0, the calculated results are as follows : —
* The Astronomer Royal lias tabulated the coordinates, for the same
value of e, on the hypothesis of the resistances varying sinii)Iv as the velo-
city, which will be found to give to the ein-ve too low a posuion, as mi^ht
have been inferred by comparing the limiting angles exhibited in the foi-e-
going Tables.
Mr. Woolhouse on the Deposit of Submarine Cables. 361
Table for e = 2, B' = 0, /5o= 1 •
1-
1-a.
.r.
y-
<1-
16
1-17351
X.
0-65203
y-
0-1/351
0
1-00000
000000
oonooo
1
101005
0142()5
001005
17
1-18530
067835
0-18530
2
1-02020
0-20349
002020
18
1-19721
0-704J3
0-19721
3
1 03045
025 138
003045
19
1-20924
0-73062
0-20924
4
104081
0-29279
0 04081
20
1-22140
0-75665
0-22140
5
1-05127
0-33020
005127 i
21
1-23368
0-78265
0-23368
6
106184
0-36488
0 06184
22
1-24608
0-80864
0-24608
7
1-07251
0-39759
007251
23
1-25860
0-83465
0-25860
8
1-08329
0-42881
008329
24
1-27125
0-86071
0-27125
9
1-09418
0-45888
0 09418
25
1-28402
0-88683
0-28402
10
1-10518
0-48805
0-10518
26
1-29692
0-91303
0-29692
11
1-11628
0-51650
01 1628
27
1-30996
0-93933
0-30996
12
1- 12750
0-54437
0-12750
28
1-32313
096574
0-32313
13
1-13883
0-57177
0 13883
29
1-33643
0-99227
0-33643
14
1-15027
0-59880
015027
30
1-34986
1-01894
0-34986
15
1-16183
0-62553
0-16183!
The extreme coordinates contained in the first Table are
37= 1-01756, ?/ = 0-34923. From the second Table, when B' = 0,
for the same value of x the interpolated value of y is 0'34917,
being only 0*00006 in defect, which would not be appreciable in
any drawing of the curve; and for higher values of e the ap-
proximation will be still nearer-
Similar Tables might be constructed for other values of e.
From equations (10), (14), and (15) wc have
T— a \\—a acosw + l/ L ^2 J
Or, putting =7,
tan
(17)
When 7 is taken equal to 1, 2, 3, &c., the values of w calculated
from this formula are shown in the followin2; Table : —
Table of Inclinations (&>).
T-a
y
e=\.
e = 2.
e = 3.
e=4.
c = 5.
e = Q.
e = 7.
1
51 49-6
28 i-3
18° 55-2
14 15-0
11 25-0
9 31 0
8 ll'-O
2
46 24-5
27 58-3
.. t.
3
40 42-4
27 30-0
18 54-8
4
36 30-7
26 39-2
18 52-2
5
33 20 8
25 40-3
18 450
14 14-7
6
30 52 0
24 41-3
18 34-2
14 13-7
7
28 51-7
23 45 2
18 200
14 11-8
8
27 120
22 53-4
18 3 5
14 90
11 24-7
9
25 47-5
22 5-6
17 460
14 5-(>
11 24 0
„ ,
10
24 34-8
21 21-6
17 280
14 00
1) 23 0
11
23 31-4
20 41-6
17 98
13 54-7
11 22-0
9 30-5
12
22 35-6
20 45
16 51-8
13 48-3
11 20-7
9 300
»> »
363 Mr. Woolhouse on the Deposit of Submarine Cables.
Ilcnce as a is a very small quantity and the tension cannot in
practice exceed the tensile strength of the cable, we conclude
that, if the depth of the sea be at all considerable, the inclination
{(o), at the ship, must necessarily be very near to the limiting
angle, especially if that angle be small.
If we consider the nature of the formula (11), it is evident
1 2
that the quantity under the fractional exponent -r- — ^ must
necessarily be algebraically positive. Therefore cos co —a and
cosftjj— a must have like signs; that is, in any possible form of
the cable, the inclination tw must either be always less or always
greater than the limiting angle X. Let us briefly examine these
two cases separately.
1. When ft) is always less than the limiting angle, the values
of cos ft) — a will be positive; and therefore the values of T — «
will be always positive. Also, since the values of cos ft) — e^ sin^ ft)
are positive, it follows from (3) that the radius of curvature is
always positive. Consequently the curve is everywhere concave
upwards and convex downwards.
The equation (12) indicates that the radius of curvature in-
creases rapidly when ft) approaches to the value of X, and that
the upper portion of the cable rapidly approximates in form to
that of a straight lime. Also the equation (14) shows that for
a given value of e, or at a given speed of the vessel, the contour
of the curve \vi\\ be given in species, the scale of measurement, or
unit, being the length of the radius of curvature at the lowest
point ; and this again will depend upon the amount of " stray
length " of cable payed out as compared with the depth of the
sea.
Now d(s—x) ds — dx 1 — cos ft) , ,
; = i = . = tanift) ;
ay dy sni w
.'. stray length s — x=-\dyi?).xi\(£). . . . (18)
As ft) is always less than \, the superior limit of this integral
is obviously 7/tan|X, or c^y. For this extreme limit we must
have ft)=X; and if this equality exist at any point v. here the
tension is finite, it must, by (11), subsist at all other points;
and the curve will therefore merge into a straight line. And by
(14) we have then Pq=0, and by (3) Tq^c, which is the least
possible value of the tension at the lowest point. But as the
curve should be continuous with the line of the deposited cable,
in order that this tension may be adequately sustained, we ought
not to pay out the stray length to the extreme limit, but only
until Pq becomes small ; for the prescribed movement of any por-
tion of the cable, separately considered, must obviously require
3 n Tt
Mr. Woolhouse on the Deposit of Submarine Cables. 363
that the due amounts of tension shall be continually maintained
at its extremities.
The cable being traced
upwards from the lowest
point soon assimilates to a
straight line, and when the
stray length is gradually in-
creased the modifications of the cui-ve will be as in the annexed
diagram, where B' D' is the direction of the ship's motion, and
A B, ac, d d successive representations of the suspended cable.
The curves being similar, A B will be a prototype of the rapidly
decreasing portions a b, a! b\ and the diminished scale of mea-
surement bringing in an increased proportion of the upper part
of the curve, it will evidently approximate to the right line m n
as a limit, where Pq becomes evanescent.
In each position of the curve we have by (3) To=rt-|-/3o> and
at the limit Tq=<7, which we have observed is the minimum ten-
sion at the lowest point. The Astronomer Royal, from con-
founding T— a with the tension T, has presumed the non-existence
of tension at this point ; and subsequently Mr. Homersham Cox,
in a paper read before the British Association, after advancing
the same assumption as an original principle, has adduced a some-
what ingenious and elaborate proof of the dynamical necessity of
the descending cable taking the form of a straight line ; but, it
will appear, both the premises and conclusion are equally inad-
missible.
2. "When w is greater than the limiting angle X, cos &) — « will
be negative, and by (11), if T — c be positive at one point, it will
be positive at all points. Also the value of cos to — e^sin^w is
negative, and by (3) p is negative, and hence the curve is always
convex upwards. But as the direction of the curve at the lowest
point (A') is not continuous with the line of cable previously de-
posited, there cannot be any stay or reaction to support the re-
quisite tension at that point, and the consequence will be a
distorted movement in this locality accompanied by an irregular
displacement and a useless and extravagant waste of a portion of
the cable. Such will be the inevitable result of a profuse pay-
ing out of the cable; and other injurious consequences may
ensue from the friction occasioned by the cable being dragged to a
certain distance along the bed of the ocean before the tension
due to a steady movement can be reinstated.
If, therefore, a Table be made out showing the weight, in water,
of any number of fathoms of cable, it will be an important and
valuable rule for practical guidance, always to moderate the paying
out so as to keep the tension a certain proportion, say one-third
or one-fourth, in excess of the weight corresponding to the
364 Mv. M. Ponton on certain Laws
ascertained dc])th of the sea. By so doins:, the tension will be
kej)t within reasonable limits, the curve will always be slightly
concave u})wards, and there will be no waste. AA'e also conclude
that the mechanical structure and dimensions of the cable ought
to be such as to enable it to bear a tensile strain of not less than
three times the maximum depth.
In calculations of distance, it will naturally occur that an
additional length of cable will be needed to accommodate the
irregularities of tlic bed of the ocean ; and it may not be un-
reasonable to entertain a conjecture as to whether or not any
extensive fissures or chasms may exist at great depths, which can
only be ascertained by repeated soundings.
Note. — The mechanical or dynamical conditions W'hich deter-
mme the subsistence of both branches of the curve of steady
movement, may be comprehended by conceiving two vessels, B' B,
to be sailing with equal velocities in the direction B'B, and that
the suspended cable curve B' A B is payed out from B and at the
same time wound up to B' with the same velocity, so as to keep
the lowest point A just on the verge of contact with the ground.
The curve will be nearly the same in form whichever of the two
be the paying out vessel ; and when B and B' are supposed to
coincide, the two branches of the curve will become duplicates of
the limiting line 7n n.
Alw)'ne Lodge, Canonbuiy,
April 5, 1860.
L. On certain Laws of Chromatic Dispersion.
Bij MuNGO Ponton, F.R.S.E.
[Concluded from p. 272.]
THE difference between the view of M. Cauchy, then, and
that arising out of the foregoing investigation, may be
shortly stated thus : — According to the former, the refractive
index of the wave corresponding to each of the fixed lines is a com-
pound quantity consisting oitivo terms, one constant for the me-
dium and temperature, the other variable and inversely propor-
tional to the squares of the normal wave-length. According to
the latter view, the refractive index is still a compound quantity,
but consisting of three instead of only two terms. One is constant
for the medium and temperature. The second is variable — not,
however, in inverse proportion to the squares of the normal
wave-lengths. It corresponds to a further shortening of the
w-ave-length beyond that corresponding to the constant portion
of the index; and these further shortenings are in strict inverse
proportion to the primary normal wave-lengths, or to the initial
forces by which these are generated. The third portion of the
index is also variable, and is that corresponding to those varia-
of Chromatic Dispersion. 365
tions in the wave-lengths whicli are rendered manifest by the
displacement of the lixed lines from their normal relative positions
in the unrefracted spectrum, and which are attendant on the
irrationality. The first, or constant, portion of the index indi-
cates the state of compression of the rether in the pores of the
medium. The variable fiagment consists of two portions, — one
depending for its magnitude on the specific action of the pon-
derable molecules of the medium on the aether within its pores,
the other apparently depending on a specific action of the vibra-
tions of the ponderable molecules of the medium on certain defi-
nite waves passing through the sether in its pores, in virtue of
which some of these waves are slightly lengthened, and others
slightly shortened, but always in a certain symmetrical manner.
To place the matter in a popular point of view : — Let the
fether be regarded as a universally diflfused clastic fluid, and
each portion of it as comprising numerous centres of elastic or
repulsive force. Since force cannot exist as a simple abstraction
(for we cannot conceive of force as being exerted by nothing, or
by mere space), it is needful to suppose these centres to be each
occupied by a something which exerts the force, and which may
be called ' an sethereal particle.' These particles must be sepa-
rated from each other by certain minute but variable distances,
otherwise there could be no movement of the particles. Each
particle must be conceived to occupy a certain normal position
in absolute space, from which it never departs except under the
influence of some applied external force, and to which it always
returns when that applied force ceases to act upon it. In the
free aither, each particle is retained in its normal position with
a certain persistence, in virtue of the forces exerted upon it by all
the other ethereal particles by which it is surrounded. The force
required to induce any given amount of motion in an ;ethereal
particle must be proportional to the degree of this persistence.
Assume, for the sake of illustration, that in the wave corre-
sponding to the fixed line B in the free aether there are em-
braced in the direction of its length 1,000,000 of such par-
ticles, that is, the moving force has time to progress onwards,
and more or less to affect 1,000,000 particles in a right line in
the direction of propagation, during the period occupied by a
single particle in performing its individual motion in this par-
ticular wave. On this assumption, the wave corresponding to
the fixed line H must similarly embrace, in the direction of its
length, 570,655 such particles. Suppose now a })ortion of the
aether to be, from any cause, so compressed as to halve the inter-
vals between its particles. When the waves B and II enter this
compressed portion, B ought still to embrace 1,000,000, and II
570,655 particles in their respective lengths; but the intervals
366 Mr. ]\I. Ponton on certain Laws
between the particles being halved, each of those waves would
now be reduced to one-half of its original length. When the
a;ther is compressed in the pores of a refracting medium, how-
ever, this rule does not hold. The B wave now appears to em-
brace in its length less than 1,000,000, and the H wave less
than 570,655 particles. If the B wave thus seem to lose, say
50,000 of its particles in the direction of its length, the H wave
will seem to lose exactly the same number ; so that this loss
tells very differently on the lengths of these two waves. The
H wave heeonies proportionalli/ more shortened by this loss than
the B wave ; so that the motive force progresses more slowly in
the H wave, in proportion to its rate of progress in the B wave,
than it did before entering the medium. Hence to keep up with
its more rapid neighbour, and present a straight front to the
observer, the H wave takes a shorter cut in passing through the
medium. It pursues a different path; the two waves become
more or less separated, and this constitutes dispersion.
Now this want of power in the motive force to extend to its full
number of particles during the period of the individual excursion of
each particle, must be due to an increase in the persistence of the
particles in their normal positions. This persistence will of course
be increased by the greater proximity of the particles ; but the
increase of persistence thence arising exhibits itself in the general
shortening of the wave-length, in proportion to the compression
of the aether. Were the additional loss of length which mani-
fests itself in the dispersion of the waves due to this cause alone,
then would the dispersive power of every medium be proportional
to the density of the aether in its pores, or to its general refract-
ive power. But this is far from being the case. The oil of
cassia, for example, which exerts a smaller compressing force on
the aether than does crown-glass, has nevertheless a much higher
dispersive power ; so that the latter must be due to some other
force than that which causes the refraction.
Su])pose now a medium in which the value of ae is 0*05, and
that of e 1*5, so making the density of the aether one-half more
than it is in the planetary spaces, the intervals between the
aethereal particles being thus reduced in the proportion of 0*66
to 1. Were there no other cause operating than this greater
proximity of the particles, and if the wave-length continued to
embrace its primary number of particles, each wave-length ought
to be diminished in this same proportion, at least very nearly so ;
for some little allowance must be made for the size of the par-
ticles as compared with that of the intervals. But it is found
that, leaving out of view that peculiar property of the medium
which exhibits itself in the irrationality, and confining attention
to its dispersive power alone, the number of particles embraced
of Chromatic Dispersion. 3G7
in the B wave on entering such a medium will appear to be only
950,000 instead of 1,000,000, while in the H wave the number
will appear to be only 520;655 instead of 570,655; so that each
of these waves has had its length curtailed by the space which
50,000 aethereal particles would occupy in this medium, in ad-
dition to the curtailment, in the proportion of 060 to 1, due to
the increased density of the sether. Now this must be owing to
the circumstance that the molecules of the medium exert on the
sethereal particles in its pores an influence such as to increase
their tendency to remain in their normal positions, to a certain
extent beyond the measure in which that tendency is increased,
by the mere approximation of the sethereal particles themselves.
By the operation of this force, the B wave has its length dimi-
nished in the proportion of 0'95 to 1, but the H wave in the
proportion of nearly 0-91238 to 1 ; so that in the case of the B
wave the loss is in the proportion of 0*05 to 1, but in the H wave
it is 0"08762 to 1, these losses standing to each other in inverse
proportion to the initial moWng forces; and the like maybe
proved with respect to all the other wave-lengths. Thus the
loss of length arising from that peculiar action of the ponderable
molecules of the medium on the aether in its pores, in virtue of
which it increases the persistence of the jethereal particles in
their normal positions, is in exact inverse proportion to the
amount of the primaiy force by which the undulation is excited;
and this is precisely what ought to be expected. The absolute
loss of length sustained by each wave from this cause is the
same, but its relative loss is in inverse proportion to its primary
length. Thus dispersion arises from the operation of a force in
virtue of which the ponderable molecules of the medium com-
municate to the ffithcreal particles, which are for the instant
associated with them, a certain amount of persistence in their
normal positions beyond what is due to the increased proximity
of the particles themselves. It is constant for the medium and
temperature; but it is specific, and independent of the size of
the pores of the medium in which the rcther is momentarily
more or less compressed; so that a high dispersive power may
consist with a low refractive power, or vice versa ; although in
general the greater the compressive power of the medium, the
greater the amount of this peculiar force.
This, then, accounts for the larger proportion of the variable
quantity which remains after deducting from the indices corre-
sponding to the fixed lines the constant which represents the
density of the nether in the pores of the medium. That variable
portion corresponds to a loss of wave-length inversely ])ropor-
tional to the primary wave-length, and may be found by multi-
plying the index by this loss, as already pointed out in the case
3C8 Ml". M. Ponton on certain Laws
of bisulphnret of carbon. But the indices thus obtained are
subject to a further correction, by the addition or subtraction of
that portion which is due to the extrusion of the fixed lines
attending the irrationahty of the spectrum.
The remaining portion of the variabk; part of the index cor-
responds to this extrusion of the fixed lines from their normal
positions, in consequence of which their mutual distances are
altered fi'om what they are in the unrefracted spectrum. This
is quite a distinct pha;uomenon from dispersion, which is simply
the greater or smaller expansion of the coloured spaces, and the
consequent greater or smaller length of the spectrum which the
medium presents. Besides the shortening of the wave, attribu-
table to the increased density of the aether within the medium,
and the further shortening which it undergoes by losing a defi-
nite number of the particles embraced in its length, it may be
still further modified by an alteration in the period of vibration
of each of its component sethereal partieles,^ — an alteration which
will cause a corresponding small variation in the length of the
wave, and in the position of the fixed line corresponding to it.
These alterations, it has been shown, always take place accord-
ing to certain determinate laws ; and the total amount of the
positive and negative extrusions is so related to the dispersive
power, that, by means of the ratio between these two, there may
be always found for the normal wave-lengths an exponent at which,
the extrusions are reduced to zero, this exponent being the above
ratio multiplied by 10"8 and added to unity. By applying this
exponent to the normals, the indices of refraction become reduced
to two terms instead of three, as already pointed out.
In explanation of the irrationality two views may be suggested.
The displacement of the fixed lines is obviously due to the cir-
cumstance that the waves corresponding to the central lines D,
E, and F arc less refracted; while those corresponding to the
extreme lines B, C, G, and H are more refracted than they
would otherwise be. There is thus a transfer of motive energy
from the extremes to the central region of the spectrum. Now
this distribution corresponds to that of the brightness ; for all
spectra are brighter towards the centre than towards the extremes.
The brightness being proportional to the squares of the ampli-
tudes of the individual vibrations embraced in the wave-length,
it follows that, at the recipient surface, the amplitudes of those
vibrations are greater towards the centre than towards the ex-
tremes of the spectrum. This correspondence raises a presump-
tion of there being some connexion between these two ph?eno-
mena. The medium may be supposed to produce a certain effect
on the amplitudes of the vibrations, decreasing them by a certain
definite amount, and increasing the rapidity of the vibration and
of Chromatic Dispersion. 369
the refrangibility of the wave by a like definite amount, as a
consequence of the curtaihnent of the ampHtude. This curtail-
ment being absolutely the same for all the waves, will produce
the greatest rateable effect on those undulations whose vibrations
have the least amplitude, namely those at the extremes of the
spectrum. Hence these will have their refraction increased from
the operation of this cause in a higher proportion than will the
central waves, and so produce a displacement of the fixed lines
from their normal positions in the manner observed.
Or again, the slight alterations in the rapidity of the indivi-
dual vibrations of the rethereal particles comprised within the
wave-length, and which manifest themselves by the displacement
of the fixed lines, may be due to a sympathetic action between
the vibrations of the ponderable atoms of the medium and
those of the eethereal particles, somewhat resembling the sym-
pathy of vibrating pendulums; and in virtue of this sympathy
some of the {ethereal vibrations may be slightly increased, and
others slightly diminished in their rate of rapidity beyond what
they would otherwise be. These views, hovvever, are merely
thrown out as hints for consideration.
While one of the objects with which the foregoing investiga-
tion is submitted to the British Association is to call the atten-
tion of its members to the curious laws governing the displace-
ment of the fixed lines, and their use in detecting errors of ob-
servation, and to bring under their notice the advantages of the
exponential law as furnishing a method of calculating accurate
indices of refraction from tolerably correct observations, the chief
purpose is to awaken those who take a lead in the proceedings
of the Association to the necessity which exists for a careful repe-
tition ot those observations that have been found most deficient
in accuracy, and for an extension of the observations generally.
It would be particularly interesting to accumulate observations
at different temperatures, so as further to illustrate the law of
the variation of the index of elasticity, viewed in relation to the
contractions and expansions of the medium under the influence
of changes of temperature, and also in rchition to the capacity
of the medium for heat. It is not imju'obable that, out of an
experimental investigation carefully conducted in this direction,
some higiily interesting and important results might arise.
It is only imder the direction and auspices of such a body as
the British Association that there is any likelihood of an experi-
mental investigation of such a nature being undertaken ; and
it is hoped that, when its importance to the science of physical
optics shall have been duly weighed by them, they will not fail
to j)lace the matter in the hands of competent and earei'ul ob-
servers, so that an enlarged store of trustworthy experimental
data may be obtained.
370
Mr. M. Ponton o?i certain Laws
Table I.— Elements of Calculation.
The media arranged according to the value of log e.
Media
log 6.
a.
n.
logf«-
an-
P. Nitrate of bismuth
0*1185050
0-009597
17
0'1214201
0*004622
F. Water, No. 1, T. i8°-75...
0*1185492
0*009687
1*6
0*1212442
0*005087 1 *
0*005087 J
F. Water, No. 2, T. i8°*75...
0*1185793
0*009645
...
0*1212442
i'. Water, T. 15 *8
0*1187071
0*1190925
0*009836
0*012365
2*0
0*1223208
0*003694
P. Muriate of zinc
P. Subacetate of lead
0*1199078
0*009548
1*8
0*1230654
0*004192
P. Nitrate of mercury
0*1210345
0*010891
0*1246282
0*004806
0*1210587
0*1213789
0*1221380
0*009894
0*009615
0*010067
T*h
0*1238184
0*1257358
0-1256868
0*005206
0*002316
0*004083
I'. M uriate of baryta
"•6
P. Superacetate of lead
1*9
P. Nitrate of potash
0*1225076
0*1225266
0*011004
0*009738
2-4
I '4
0*1273767
0*1246065
0*002970
0*006206
P. Sulphate of magnesia ...
P. Nitrate of lead
0*1227524
0*1240384
0*010397
0*010655
1*8
0*1262004
0*1275798
0*004583
0*004701
P. Muriate of ammonia
1*8
P. Alcohol, T. i7°*6
0*1288364
0-1315513
0-1370585
0*1389150
0-1392094
0*009368
0-010312
0*014199
0*012103
0*013901
17
0*1317568
0" 13 5459 3
0*1427913
0*1433528
0*1422945
0*004504
0*003869
0-004907
0*004911
0*008862
P. Nitric acid
P. Muriate of lime
1*9
1*4
P. Muriatic acid, T. i8°*6 ...
F. Sol. of Potash, T. 2i°*5 ...
0*1392960
0*011002
i"7
0*1428138
0*005287
0*1396349
0*1398999
0-012410
0*011513
T-6
0*1432346
0*1424568
0*006549
0*007341
P. Solutionofpotash, T. 16°.
I '4
P. Sulphuric acid, T. i8°*6 ..
0*1502045
0*009301
1*0
0*1502375
0*009259
F. Oil of turpentine, T. io°*6..
0*1585949
0*013758
2*1
0*1644359
0*004751
R. Calc-spar ex. ray
o*i66io5ii
0*1671802
0*1695691
0*1966605
0*002824
0*006945
P. Oilofcassia.No. 3,T.22°*5.
0*049533
r4
P. Oil of sassafras, T.2o°*9 ..
0*1680534
0*023053
2*7
0*1810982
0*005144
P. Oil of anise, T. 2o°*9
0*1683381
0*030529
2*8
0*1847136
0*006356
P. Oilof cassia, T. 14°
0*1688690
0*048800
rs
0*1982254
0*006483
P. Oil of anise, T. i5°*i
0*1695285
0-030191
2*8
0-1857498
0*006297
P. Oil of cassia, T. 10°
0-1695982
0-048723
3*2
0*1978781
0*007803
P. Oil of anise, T. i3°*25 ...
0*1698189
0*029579
2*8
0*1857218
0-C06I65
P. Creosote
0*1699152
0*1755898
0*022836
0*011225
2*5
1*9
0*1813500
0*1800728
0*005855
0*004550
F. Crown-glass No. 13
F. Crown-glass No. 9
0*1759127
0*011384
1*9
0*1804622
0*004615
P. Rock-salt
0-1771542
0*1785369
0*015460
0*Co8l22
0*1842930
0*1817994
0*004942
0*003291
R. Arragonite, 1st axis
1*9
R. Quartz 0. ray
0*1814768
0*1819878
0*009365
0*038772
1*7
2*5
0*1847752
0*2021429
0*004501
0*009949
P. Bisulphide of carbon
F. Crov.n-glass M
0*1828213
0*1838501
0*1915881
0-1961852
0*1967997
0*013003
0*009541
0-018721
O-O2OI7S
0*020402
0*1883987
0*1872281
0*2005423
0*2059514
0*2066932
0*004857
0*004586
0*005986
0*006450
0*006518 "1 *
0*006518
P. Quartz ex. ray
F. Flint-glass No. 3
F. Flint-glass No. 30
F. Flint-glass No. 23 (2) ...
2*2
F. Flint-glass No. 23 (i) ...
0*1968160
0*020382
2'2
0*2066932
F. Flint-glass No. 13
0*1970545
0*2004488
0*2010442
0*2029670
0*020502
0*008465
0*008421
OC08466
O-OI4IO7
0*013062
0*2066058
0*2035624
0*2041424
0*2063425
0*2142084
0*2205295
0*007080
0*004069
0*004051
0*003735
0*005719
0*005297
R. Topaz, 2nd axis
R. Topaz, 3rd axis
R. Topaz, ist axis
rS
R. Calc-spar 0. ray
i"9
1*Q
R. Arragonite, 3rd axis
0-2148137
R. Arragonite, 2nd axis
0*2156888
0*013330
2*0
0-2218703
0*004971
F = Fraunhofer. P = Powell. R = Rudberg.
* Mean of two observations.
'Note. — The elements lop; tn, an, and n are the three from which the
indices in Table VI. are calculated. The elements loge and a are those
from which the wave-lengths iu Table III. ai-e calculated.
of Chromatic Dispersion.
371
Table II. — Internal Wave-lengths calculated from the observed
Indices (corrected by the laws of extrusion) per formula — = u.
Media in same order as in Table I.
Media
Space..
Nitrate of bismuth ...
Water(i),T.i8°-75....
Water(2);T.i8='75....
Water, T. i5°-8
Muriate of zinc
Subacetate of lead. ...
Nitrate of mercury....
Sulphate of soda
Muriate of baryta
Superacetate of lead..
Nitrate of potash
Sulphate of magnesia.
Nitrate of lead
Muriate of ammonia..
Alcohol, T. i7'*6
Pyroligneous acid
Nitric acid
Muriate of lime
Muriatic acid
Sol.potash,T.2i°-s....
Solution of soda
Sol. potash, T. I6^...
Sulphuric acid
Oil of turpentine
Calc-spar ex. ray
Oil of cassia, T.22°*5..
Oil of sassafras
Oil of anise, T. zd^'g..
Oil of cassia, T. 14°....
Oil of anise, T. i5'^-i....
Oil of cassia, T. 10°....
Oil of anise, T.13^'25..
Creosote
Crown-glass No. 13...
Crown-glass No. 9 ...
Uock-salt
Arragonite, istaxis....
Quartz 0. ray
Bisulphide of carbon.,
Crown-glass M
Quartz ex. ray
Flint-glass No. 3
Flint-glass No. 30 ....
Flint-glass No. 23(2).
Flint-glass No. 23(1).
FHnt-glass No. 13 ....
Topaz, 2nd axis
Topaz, 3rd axis
Topaz, ist axis
Calc-spar 0. ray
Arragonite, 3rd axis...
Arragonite, 2ndaxis...
B.
I "000000
b.
C. D.
0-953893 0-856059
c. d.
751542
751350
751328
750920
749008
749064
745825
746734
746378
744657
743108
744380
743216J0
740796,0-
7337830-
728385
714899
713980
'711737
■714475
•7I2458JO-
•713063
•698275
•680043
'673900
■629128
■655438
■647207I0
•627156
•645744
•626449
■645912
-652742
-656034
■65538010'
.649222I0
-65466510
-648971 jo
■617971,0
•64318CJO
-645203 o
■62420310
■6159270
■6I4793J0
■6147810
-6I4345I0
■621736:0
■62C925I0
•61808510
•604925:0
•5965520
•595026 o
7I6406JO'
716291
716293
715815
7"755
714153J0'
710853I0'
7ii94i|o'
711546I0'
7099oi{o'
7082660'
7096370'
7086301O'
706169
699693
693994
681450
680574
678449
681102
679464
679605
665708
648233
642569
598803
624480
616489
596967
61509S
595923
615257
'622037
62538110'
'624746
'618S08
■624194
■618688
■588133
■61307c
•615098
594771
-586839
-585767
585762
585325
59273S
591966
-589261
■576545
-56853S
-56712c
E. F.
0-764567 0-704210
■642103 o-
'641927 o-
■64I927o-
'641571I0-
'637S5c!o^
'64oi2iio^
'6369960'
6379430-
6378480-
636238 o-
■63475lo-
■6359070-
■6349730-
■632758
■626965
■622136
610336
■60972S
'607368
'610248
•608197
•608817
■596515
-580602
-5759660
-534169
•558749
•551087
-532607
•549742
•531582
•54999c
■556497
560254
559667
554160
559479
'•554371
-524932
-549081
•551123
1-532211
1-525001
1-524010
1-5240 II
'■523572
1-531186
'■530494
1-528073
1-516164
1-509073
1-507776
G.
0-623398
5724950-
572345
572343
572108
568703
570654
567945
568789
56896c
567187
565924
566935
566093
564172
559095
5546370'
5437i3io'
543402jO'
541091 o'
5439340'
5418990'
542590:0'
5316910
5171760'
5135830
4727140
■•489388
1^47 1 748
1-488261
1-470532
1-488541
1-494800
'•499267
'■498737
'■493330
5-494194
'■465125
1-489117
)-49i272
'■473553
3-466955
>-466o44
3-466062
3-465621
3-473564
3-472916
3-470765
'•459589:0
3-4334020
3-4521930
526556
526387
526399
526087
522954
52488c
52214c
523112
522956
521715
520346
521483
520548
518755
514172
510039
499724
499475
497310
500120
498254
•498839
■489035
■47526c
•472402
•431660
•455858
•448342
-430499
•447317
•429685
-447601
•453890
•458967
•458455
■453126
-458829
•454446
■425376
•449475
■451735
-434687
-428491
-427629
■427635
■427245
■435504
•434939
432961
-422189
416569
415439
H.
0-570655
h.
Stun.
5-472782
0-464874 0-424688 4'
o'464774|o-424538|4'
0*464785 0-424 543 !4'
0-4642I7JO-424337J4'
0-461742 0-42 1645 14-
o"463389'o-4233i5J4'
0-4608 200-4208 37 14'
0-4618140-4218304'
0-461635 0-42 1 74 1 [4'
o-46o48o:0'42C495:4-
0-4588530-4193514
0-460412 0-420527 4'
o'459462.o-4i96oo 4
0-45780810-4 1 S062 4
©■45394iio"4i4689!4
o-450i72'o-4iioi6
0-440408 0-40 1 700
0*440564 0-402 152
0-438485 0-400158
0-4413190-402900
o*439598'o-40i273
0-44019 110-401898 [3
o'43i7i6|o-39456i|3
0-418894:0-381996 3
o*4i7i28'.o'38o995 3
o"374976|o^335976
0-4C0255J0-363636
0-39254310-355482
o-37394iio-335i86
o^39i778jo^354796
o^373337Jo-3349ii
0-3920490-355194
o-3986i7lo-362343
0-40482S 0-369431
0-404369 0-368982
o'399052'o-363684i3
0-4051 18 o'37O026j3
0-401 io5'o-366227J3
o-37ic92|o-335285'3
o'396i77'o36i295,3
0-39869410-364007,3
0-382272,0-347881 3
o-3765S3io-3425i5 3
0-375801
0-375802
0-375476
0-384457
0^3417753
0-341774,3
0-341492 3
0-351086 3
0-383960 0-3 50654] 3
o-382i7i|o-349C03'3
0-37191110-33900913
0-36705010-334675:3
0-3660160-333697 3
098664
097612
097618
095055
073657
085576
065416
072163
071064
060673
050599
059281
052522
038520
C02338
970379
89223c
'889875
'874598
'894098
•881143
•885C03
•807501
•702204
•676543
•377426
■555305
•500538
■36S1C4
-492736
•362418
•494544
•54C926
•574162
-570336
•531382
•571179
•538CC2
•327914
■501395
-517132
•38958c
-342311
•335819
•335827
•353076
•39C271
•385854
■370317
•29C332
•245S59
•237267
37.2
Mr. M. Ponton on certain Laics
Table III. — Internal "Wave-lengths, freed from the extrusions,
calculated by formula a = u.
Media in same order as in Table I.
Media
Space
B.
I'OCOOOO
Nitrate of bismuth o
Water, No. i, T.i8°-75.. o
Water, No. 2, T.i8-'75..'o
Water, T. 15^-8
Muriate of zinc
Subacetate of lead
Nitrate of mercury
Sulphate of soda
Muriate of baryta
Superacetate of lead ..
Nitrate of potash
Sulphate of magnesia ..
Nitrate of lead
Muriate of ammonia ..
Alcohol .-.....,
Pyroligneous acid
Nitric acid
Muriate of lime
Muriatic acid
Sol. of potash.T. ai°-s
Solution of soda
Sol. ofpotasli,T, 16°..,
Sulphuric acid
Oil of turpentine ,
Calc-spar ex. ray
Oil of cassia.T. 22°'5 .
Oil of sassafras
Oil of anise, T. 2o°*9 .
Oil of cassia, T. 14° .
Oil of anise, T. i5°-i .
Oil of cassia, T. 10° .
Oil of anise, T. i3°'25.
Creosote
Crown-glass No. 13 .
Crown-glass No. 9 ....
Rock-salt
Arragoiiite, 1st axis .
Quartz 0. ray
Bisulphide of carbon .
Crown-glass M lo
Quartz ex. ray lo
Flint-glass No. 3 ^c
Flint-glass No. 30 ...
Fhnt-glass No. 23 (2)
Fhnt-glass No. 23 (i)
Flint-glass No. 13 |o
Topaz, 2nd axis o
Topaz, 3rd axis lo
Topaz, I St axis jo
Calc-spar O. ray o
Arragonite, 3rd axis ... p
Arragonite, 2ud axis ... o
C.
0-95389:
C2-
•7515960'
•751429O'
■7514180'
■7510030'
■7477990'
■749191 o'
■745882p'
•746836]o'
•746558
■744785
•743206
■744439
■743388
•740901
■73393110
•72835510
•7i5i6c|o
•7141450
•711855
•714609
•712635
•71309c
•698311
•680315
•674053
•630954
•656067
•648146
•629046
■646626
•627986
•646786
•653379
•656212
■655557
■649577
•654801
649086
618904
643412
[•645 321
624577
■616346
•6l5222'o
•6i52i8|c
•614749
621841
'621021
618195
605154
596736
595241I0
'7165CC O'
'716336 o
'716328 o
'7159240
'712751
'714208 o
71099c
7II947
'711693
709982
708432
709667
■708634
■706251
'69966c
'694298
■681532 o
■680660 o
•6783930
■681154
'679206
■679681 o
■6656S6 o'
■6483140'
■642600 O'
■599579 O'
■624755
■616855 o
■5977930
•6154210'
•596785|0'
"6156010'
•622201 o
•625439JO'
•6248o7io'
■618914:0'
•524236J0'
•618727,0'
•58858i}o'
•613147 o'
■615128 o'
■5949160'
•586998,0'
■585916,0'
•585913:0'
•585460 O'
•5927790'
■5920CO o'
■589302|0'
•576602,0'
•5686210'
■567182J0'
U. I E
3-856059 0-764567
642029
641873
641 8 7c
641487
63838c
639977
636951J0
63791210
637713I0
63613 no
534644J0
635882
634887
632721
626940
62203c
610175
609608
607389
610164
608271
60879c
596457
580409
57586c
533004
558314
550457
531476
549204,0
5305791O
5494
'556044I0
'560140:0
'559557
553851
559379
'55430710
'524238
548927
551060
'5319790
'524724
'52373c|o
523729,0
5233100'
5311140
5304190
527993|o
516017 o
508961 o
5076430'
F.
o'7042ic
f2-
572386
572237
572239
571876
568831b
570558
567712
568677
56853c
567068
56564c
G.
©•623398
i'565922
1^563960
'•558934
.•55444S
'■543445
i'543i62
(•540988
'■543776
'■541935
,•542494
)'53i7]6
)"5i6907
'■513447
'■470745,
!-496i8cp
(■4883630
>-469459io
.872Si|o
)-468666 o
'■48754710
)-494i76 o
'499075 o
'4985370
'■493005 o
'■4987270
>-494o64 o
)-464c65
)-48887o
3-491145
.•473123
(•466487
'•465575
'■465577
)-465i9c
'■473446,0
)'472830jO
i'47o658jO
>'45936ojo
'■45317010
'•451963,0
•526443
•526299
•5263C4
■525955
•5229500'
•5247640'
•522036I0'
•52300310
•5228900'
•5215080'
•5201 i9'o'
■521361:0'
•5204260
•5185990
'•5140710'
•50986510
'•499423:0
'■499328JO
-•4971840'
H.
0-570655
A,.
464929
464791
4648C0
464470:0
'46152CJO
46 3448 p
Sum.
5^472782
498174
'49876c
'489007
'475015
•472273
'429673
'455190JO
•447401.0
•428546,0
•4464310
•427822b
•446724^0
•4533620
•4587910
•458283
■452866
•458715
'454323
■42437c
■44925 ilo
■4516200'
■434296,0'
■428069 ^'
'427211
'427214
'426848
'435403
'434839
'432835
421983
'4I636410
■415232 O'
461850:
461782
460506
459169
460414
4595"
457864
454003
450171
440482
440638
4385340
441 343 jo
4395820
440203J0
431823
418926
417145
'374681
•4C0309
■392556J0
3737680
3917350
3731360
3920650
3987150
4048 54|0
404386
399123
305143
40 1 1 1 2
371222
396205
398699
3823C9I0
37663c
375845
37585c
375512
384466
383972
382193
371939
3670S5
366052
'•4247814"
'•424647:4'
;-424659|4-
'■4243404'
(-421426 4'
(•423430,4'
;*42C965 4'
(•4219384'
(•421898,4'
(-420693 4'
(•4193894'
(•420637 4'
'■4i9754:4'
(-4i8224'4'
>-4i4799;4'
3"4i 1212 3'
(•402013
(•402334
(•400255
(•403071
'■4013403
.•401985
'•394501
•382318
•381165
•338790
•36449c
■356750
•338016
•356038
'•337444I3
•356392I3
'■363049 3
•369651
•369209
-•364046
.•370178
•366383
'■336534
.■361583
■364159
-34838c
'•343057
(-342320
'•342326
'•342007
(-351222
(-350773
'■349141
'■339277
'■334922
'•333954
09S664
097612
097618
095055
073657
085576
065416
072163
071064
060673
050599
059281
052523
038520
002338
970379
892230
889875
874598
894098
881143
885003
807501
'702204
676543
377426
555305
500538
■368104
•492736
362418
494544
540926
574162
•570336
•531382
571179
•538002
327914
501395
517132
389580
342311
335819
335827
333076
390271
385854
'370317
290332
245859
237267
of Chromatic Dispersion.
373
Table V,* — Logarithms of the Wave-lengths of tlic fixed lines for each
exponent from 1 to 3-5, that of B being =0. Also the Logarithms
of S and A.
n.
C.
D.
E.
F. ! G. II.
S.
A.
i*o
I_ i_
1-9794999 11-9325036 1-8834154
1-847702411-7947653 !r7563732 0-7382081
0-3224004
i"i
I '9774499
1-9257540. 1-8717569
1-8324726 1-7742418 1-7320115
0-7284077
0-3531264
ra
'■9753999
1-9190043 1-8600985
j
1-8172429 1-7537184 1-7076478
0-7187648
0-3799546
i'3
1*9733499
1-9122547 1-8484400
1-8020131 1-7331949 1-6832852
1
0-7092784
0-4040377
'•4
1-9712999
1-9055050 ;i-83678i6
7-7867834
1-712671411*6589225
0-6999472
0-4256320
I'S
1-9692498
7-8987554 1-8251231
7-7715536
7-6921479 1-6345598
0-6907696
0-4450947
1-6
1-9671998
1-8920058
1-8134646
1-7563238
1-6716245 1-6101971
0-6817445
0-4627112
17
1-9651498
7-8852561
i-8oi8c6i
1-741C940
1-6511010 1-5858344
0-6728703
0-4787166
1-8
1-9630998
1-8785064
1-7901477
7-7258643 1-6305775 1-5614717
0-6641455
0-4933033
1-9
i'96i0498
1-8717568
1-7784893
1-7106346 1-6100524 1-5371091
0-6555684
0-5066368
2*0
1-9589998
1-8650072
7-7668308
1-6954048
1-5895306 1-5127464
0-6471379
0-5188511
2*1
1-9569498
7-8582576
1-7551723
1-6801750
1-5690071 1-4883837
0-6388519
0-5300649
2'2
7-9548998
7-8515079
17435139
1-6649453
1-5484837 1-4640210
0-6307087
0-5403794
i'3
1-9528498
7-8447583
1-7318554
1-6497155
1-5279602 7-4396584
0-6227067
0-5 98820
2-4
7-9507998
7-8380086
1-7201970
1-6344858
7-5074367
7-4152957
0-6148442
0-5586479
i'S
1-9487497
1-8312590
7-7085385
16192560
1-4869132
7-3909330
0-6071192
0-5667425
2-6
7-9466997
1-8245094
1-6968800
1-6040262
7-4663898
7-3665703
0-5995298
0-5742271
27
1-9446497
1-8177597 1-6852215
1-5887964
1-4458663
1-3422076
0-5920745
0-5811524
2-8
7-9425997
1-8110100 1-6735631
7-5735667
1-4253428
1-3178449
0-5847512
0-5875643
2-9
7-9405497
1-8042604 1-6619047
7-5583370
1-4048177
1-2934823
0-5775580 0-5935051
3-0
1-9384997
1-7975108 1-6502462
7-5431072
1-3842959
1-2691196
o*5704933 0-5990105
3-1
7-9364497
1-7907612
1-6385877
1-5278774
1-3637724
7-2447569
0-5635547 0-6041158
3'a
'•9343997
1-7840115
1*6269293
7-5126477
1-3432590 1-2203942
0-5567408 0-6088483
3*3
1-9323497
7-7772619
7-6152708 :7-4974i79
1-3227255 '1-1960316
i
0-5500483 0-6132386
3 "4
1-9302997
1-7705122 1-6036124 1-4821882
1-3022020 1-1716689
0-5434768 0-6173097
3'5
[-9282496
7-7637626 7-5919539
1-4669584
1-2816785 1-1473062
0*5370234 0-6210834
* Table IV. will be found at p. 376.
Phil, Mag, S. 4. Vol. 19. No. 128. May 1860. 2
C
Table VI. — Indices of Refraction calculated from the exponential law.
Formula w = r — ■ •
— —On
Media of each observer arranged in the order of agreement with the observed indices.
I. Fraunhofer's Observations.
Media
Crown-glass No. o ...
^Yate^, i&2,T.i8^75,
Crown-glass M
Sol. potash, T. 2i°"5.,
Crown-glass No. 13...
Oil of turpentine
Flint-glass No. 13 ...
Flint-glass No. 30 ...
Flint-glass 23 (1&2).,
Flint-glass No. 3
'"B.
'^C.
i"9 i-525844'i
i"6|i*330989 I
2"o i'55477o|i
1711.399639:1
r9jr5243i4 i
2'i i"47048o I
2'i i'627729 I
2*2|i"623550 I
2*2li'62657i I
2*2 I*602092 I
11
•526852
•331697
■555933
•400504
•525306
■471553
•629686
•625451
•628424
•603775
'^D.
1-529542
i"333540
1-559063
1^402777
r527953
I "47445 6
i^635ooo
1-630547
1-633533
i'6o8379
t'E.
533024
335843
563160
405653
■531382
■478303
■642060
•637391
•640573
•614559
MF.
'^G.
'*H.
•536085 I
•33780711
•566794I1
•408131 I
■534391,1
•48175011
•648408 1
•643604 1
•646877'!
•62015611
541629 1
341252 I
573463:1'
4125261
539846I1
4881341
660210 I
'655276,1
•658723'!
•63068611
•546569
•344221
•579467
•416357
•544704
•493940
•671017
•666079
•669683
6404 I c
II. Rudberg's Observat
Topaz, 2nd axis [vj 1^608405
Quartz ex. ray '1-7 i-549902!
Arragonite, ist axis...ji'9 i^527485
Quartz 0. ray 1^7 i'5409o8
Topaz, 3rd axis ]i'7 i^6!052i
Calc-spar O. ray 'i^9 1-653084
Topaz, ist axis i^8 1^617927
Arragonite, 3rd axis.. 1^9 1^676367
Calc-spar ex. ray 2'i 1^483833
Arragonite, 2nd axis.. 2^0 i^68o675
i^6o9285|i
1-55082211
i^528207Ji
1^541804 1
i^6ii4oi[i
^■654553'i
i^6i8796ji
r677763,i
I ■48448 31
i'682o65'i
611591
553239
530127
544146
613706
■658471
■621088
•681494
•486237
•685810
•614518 I'
•5563001'
■532614 !■
•547111 r
•616623 I
•663547 r
•624025 I
-686332I1
•488558 1
•690713 1
617030 I
5589331
534790|i
549672J1
61913011
668019 1
6265741
690584 1
490630 I
695067 1
•621493 !■
■563608'!'
53873i|i'
554199 I'
■623580ji*
■676133,1'
631148 1'
■698302I1'
■494464k
•703061 I
625370
567675
542241
558148
627457
683372
635168
705182
497945
710266
III. Powell's Obser\at;
Sulphate of magnesia
Oil of anise, T.2o"^9.
Oilof anise, T. 13 "•25..
Sol. of potash, T. 16^..
Sulphate of soda . ..
Nitrate of lead
Superacetate of lead.
Nitrate of bismuth ...
Nitric acid
Subacetate of lead ...
Oil of sassafras ... ..
Alcohol
Muriate of lime
Muriate of ammonia.
Oil of anise, T. i5'^i.
Muriatic acid
Sulphuric acid
Rock-salt
Nitrate of mercury ...
Creosote
Pyroligneous acid ..,
Bisulphide of carbon.
Water, T. i5"'^8
Oil of cassia, T. 14°..
Solution of soda -
Muriate of baryta ..
Nitrate of potash ,
Oil of cassia, T.22^^5.
Oil of cassia, T. 10° .
I "4 I
2^8 I
2-81
1^4 1
1-6 1
r8 1
r9|i
r7
2^1Il
r8
^■7!
i-7|r
i'9
r8 1
2^8[l'
r4|i
i^o 1
2"2'l'
i-8!i
^•5
2-0
^•5
2^0
3*5
v6
vb
z-4
3^4
3^2
•343422
•545105
•548273
•402507
•339170
■345458
•342956
•330709
335024
525786
362743
400651
349979
548690
404948
432051
540232
340966
531891
■373285
618343
331840
594749
■403485
340125
346201
590247
596819
i'344i87
1^547251
1-550374
1^403496
i*339902
1-346195
1-343646
^■33i393
1^399823
i'335687|
1-5274161
1-3634431
1-401556
I-350740J
1^550828,
1-406 17 3]
1-432967
r54i5i6j
i"34i733
i"5336i3
1-374007
1-621648
1-332489
1-597716
1-404500
1-340651
1-346845
i^593i84
1-600068
-346148:
■5534231
■556375,
•40602 7j
•341811
-348142!
■345491
■333189I
•4025371
■3374401
•5320541
•365277
•403968
■3527391
•556970
•409243
■435250,
■545027,
■343764
■533443;
■375950
•630847:
•334233:
•606756
'407139'
•342136
•348638;
•602443
•609743'
•348551
•562296
•565013
■409125
■344198
■350631
■347874:
■3354581
■406129
■339683
■5386671
■367599
■407090
■355323
•565803
•413004!
■437921!
■5497301
■346359
■545H5
■378490
•643690
■336515
•620875
■41044!
•344210
•351086'
•616743
•624364
1^350559
1-570857
i'573344
1-411722
1^346232
1^352798
^■349964
I-3374I2
r40935i
i"34!632
1-544915
1-369596
1-409835
^■357559
1-574323
1-416155
1^44007 1
1-553990
1-348614
1-55I414
1^380744
r655795
1*338534
1-635542
1-413263
1-346159
'■353342
1^631466
'■639132
i"3 54008
i*588o79ii
i^590098 1
1-416183 1
1-349805 I
1-356678 1
'■353753|i
1-340879
1-4x5348
1-345121
1^557347
1^373138
i^4i48o3
1-361568
1-591457
1-421578
1-443612
1-561969
1-352660
1-563568
1-384860
1-679461
1-342229
1-667645
1-418217
1-349946
1-357648
1-663353
1-670436
1-356922
[•605172
[•606710
•419953
•352882
•360093
-357118
t-343892
[•420740
[-348190
[•569485
[-376218,
[-419233
1-365098
[•608423
[-426167
[•446482
[•569323
[•356220
[•575199
[•388566
[•702390
[•345546
[•702529
[•422492
'■353572
[•361690
[•697635
[•703372
Oil of Anise further cor
ected fo
Temperature.
Oil of anise, T. i3°-25.*2-8 1-548290
Oil of anise, T. i5°-i.|2-8 r548673
Oil of anise, T. 2o°-9. 2^8 i^545i2o
1-550380
i'55o8i4
'•547265
-556382
-556958
•553430
■565013 1-573410
565798k574320
■56229611-570850
1-59008011-606673
1-591476 i^6oS50o
1*588052 I^605I22
Table VII. — Observed Indices of Refraction.
Media of each observer arranged in the order of agreement with
the exponential law.
I. Fraunhofer's Observations.
Media
Crown-glass No. 9 ..
Water, No. 2
Crown-glass M
Solution of potash ..
Crown-glass No. 13..
Water, No. i
Oil of turpentine
Flint-glass No. 13 ..
Flint-glass No. 30 ..
Flint-glass N0.23 (2).
Flint-glass No. 3
Flint-glass No. 23(1).
f^B.
1-525832
1-330977
i"S54774
1-399629
1-524312
1-330938
1-470496
1-627751
1-623570
1-626564
1-602042
1-626596
'^C.
'*D.
1-526849'
i'33i709|
i"555930|
1-400515
1-525299;
1-331712
1-4715301
1-629681
1-625477
1-628451
1*6038001
1-6284691
1-529587
i'333577
1-559075
1-402805
1-527982
1*333577
i'474434
1-635036
1-630585
1-633666
1-608494
1-633667
*"£.
f^F.
'^G.
1-533005
i"335849
1-563150
1-405632
1-531372
1-335849
1-478353
1-642024
1-637356
1-640544
1-614532
1-640495
1-536052 I
1-337788 I'
1-566741 I'
1-408082 1'
1*534337 I'
1-337818 1
1-481736 1
1-648260 1'
1-643466 I
1-646780 I
1-620042 1
1-646756 1
'^n.
541657
341261
573535;
412579
5399°^,
341293
488198
660285
655406
658849
630772
658848
1-546566
1-344162
1-579470
1-416368
1-544684
1-344177
1-493874
1-671062
1-666072
1*669680
1-640373
1-669686
II. Rudberg's Obser^•ations.
Topaz, 2nd axis
Quartz ex. ray
Arragonite, ist axis.,
Quartz O. ray
Topaz, 3rd axis ....,
Calc-spar 0. ray ....
Topaz, I St axis .....
Arragonite, 3rd axis
Calc-spar ex. ray....
Arragonite, 2nd axis
i-6og4
1-6093
1*6116
1*6145
1-6170
i"5499
1-5508
i'5533
i"5563
1*5589
1-5275
1*5282
1*5301
1*5326
1*5348
1*5409
1-5418
1*5442
1*5471
1*5496
1-6105
1-6114
1-6137
1-6167
1-6191
1-6531
1-6545
1*6585
1-6636
r668o
1-6179
1-6188
1-6211
1-6241
1-6265
1*6763
1-6778
1-6816
1-6863
1*6905
1-4839
1-4845
1-4863
1-4887
1*4907
i-68o6
1-6820
1-6859
1-6908
1*6951
1*6215
1*5636
5388
1*5542
1-6236
1-6762
1-6312
1-6984
1*4945
1-7032
1-6254
1-5677
1*5422
1*5582
1-6274
11-6833
I1-6351
11-7051
1-4978
|i*7ioi
III. Powell's Observations,
Sulphate of magnesia.
Oil of anise, T. 2o°*9..
Oil of anise, T. 1 3°'2 5..
Sol. of potash, T.i5"..
Sulphate of soda
Nitrate of lead
Superacetate of lead ..
Nitrate of bismuth ...
Nitric acid
Subacetate of lead ...
Oil of sassafras
Alcohol
Muriate of lime
.Muriate of ammonia..
Oil of anise, T.i5°-i.,
Muriatic acid
Sulphuric acid
Rock-salt
Nitrate of mercury ...
Creosote
Pyroligneous acid ...
Bisulphide of carbon..
Water, T. i5''-8
Oil of cassia, T. 14°,..
Solution of soda
Muriate of baryta ...
Nitrate of potash
Oil of cassia, T.22^-5..
Oil of cassia, T. 10°.. .
1*3434
1*5451
1-5482
1-4024
1*3392
1*3455
1*3429
1*3306
1-3350
1*5^57
1-3628
1*4006
1*3499
1*5486
1*4050
1*4321
1*5403
1*3408
1*5320
1*3729
1-6182
1*3317
1*5945
1-4036
1*3398
1*3457
1*5895
1-5963
1*3442
1*5473
1-5504
1*4036
1*3398
1-3461
1*3437
1*3315
1*3998
1*3357
1*5275
1-3633
1-4016
1-3508
1-5508
1*4060
1-4329
1*5415
1-3419
1*5335
1*3745
1-6219
1-3326
1*5979
1*4039
1-3406
13468
1*593°
,1*6007
1*3462
1*5534
1*5565
1*4061
1*3419
1*3482
1*3455
1*3332
1*4026
1*3373
1-5321
1*3654
1-4040
1-3529
1-5572
1-4095
1*4351
15448
1*3439
1-5383
1-3760
1-6308
1*3343
1-6073
1*4075
1-3421
1-3487
1-6026
1-6104
3~cY
1-3486
1-5623
1*5650
1*4091
1-3442
1-3506
1-3480
1*3355
1-4062
1*3398
1*5387
1-3675
1-4070
1*3552
1-5659
1*4130
1*4380
1*5498
1*3462
1-5452
1-3785
1-6438
1*3364
1-6207
I -4 109
1*3438
1*3510
1-6174
1-6249
1-3504
1*5707
1*5733
1*4117
1-3462
1-3528
1*3498
1*3374
1-4092
1*3417
1-5448
1-3696
1*4099
1*3575
1*5743
1*4160
1*4400
1*5541
1*3487
1*5515
1-3807
1*6555
1-3386
1*6358
1*4134
1*3466
1*3533
16314
1-6389
1*3540
1*5881
1*5901
1*4162
1*3499
1*3568
1*3538
1-3410
1*4155
1*3453
1*5575
1*3733
1-4150
1*3617
1*5912
1-4^17
1*4440
1*5622
1-3528
15639
1-3848
1*6799
1-3429
1*6671
1*4181
1-3504
1*3586
1*6625
1-6698
1*3570
1*6053
1*6066
1*4199
1*3528
1-3600
1*3571
1*3437
1*4206
1*3481
1*5693
1-3761
1-4190
1*3650
1*6084
1-4261
1-4463
1*5691
1-3560
1*5749
1-3884
1-7020
1-3448
1-7025
1-4221
1*3531
1-3608
1-6985
1-7039
3rG
Mr. ]\I. Ponton on certain Lmvs
NNr*c<Mc<rlc<tnc^mmromi
't^•^■^•<i•■^^^^*J^^^^ LOO O vO i^ t^oo O O
o M -4- "~i
+I+I+IH-I+I-H+I+I+I-H+I+I+1+I+I+I+I+I+I+1+I+I+I+I+I +1+1+1+14-1+1+1+1+1+1+1+1+1+1+1+1-
O r^, ooo vo 0\vo nrloovo ri »oo -i-MOO rie-o too t-~rt t~> t^oo oooo t-~M rort C\»jiiop» rl^o rj-oo oo
'"'aQOO'-'"'roc?>"^fo"^"^'-it^"^r^N>oc?\ r^^^00T^ vovo toco ion "vo O" ■^^loo mcvt^
I 1 1 I 1 I I I I I 1 1 I 1 I I I II I I 1 1 I 1 I II 1 11 I 1 I 1 1 I 1-1 I
I 1 1 1 1 I M 11 1! I I II 1 I 1 I I I 1! 11 1! 1 1 I 11 11 I I! I 1
s"
+++++++-
■+++++++++++-
-+++++++++-
'i-'O oe rt •<i-vo CO O(~»uio mvovo woo ^o^^ t?\rt n o O r) O CN^l-t^O ooo u^ ri w ooo to ■r^ o •>1- >n •
u-icr\0 >-• OOO "I o c^ O cOT^-CNCor^ioroi-f ii roCNO '^■tOfOrlOO ^ coso ^O cl ro covo v^ OO rt O O H ^
O wMHi nMi-iMi-ii-i >-<i-<>-<r<r)i-ir)i-iHr^r4Nr4r4c4'4-r4r<co'ri-<^'<^'<^ -^vo t^ cs O
M r< u-i to vi^ t^ r^ t^vo OOO o ^ooooo ^coooo »-< *-> c* »-• to-«^o »^co cnvo o tovo oo t^oo *o covo to
O Miiix 11 ■liiiiiiiiMiitiiiMiitOMMc4Ht4'4-'^ 10\0 ^
■+ + + + -
tot^Tj- roto^cstO'4-tOTi'into lotoooooo v^vo 00 CO o rnvD t^^oooo o »i-ro'^>j-> vovo r^ ^vo
O M M WH MHWMMMllt^tOtO*
I 1 1 1 1 I I I 11 I 1 1 1 I I 1 1
C\ t^ O H O >0 lo Tj-00 O >oO r^ CO rJ -ij- r^ looo coco t^ vo ■<i- m c\oo c) o r* ►^ io-!j-^c\ONr^t^Cv^C\«
•ON t^o OnCnO lO" '-' "-> ton trit^mij-io rloo r~- i^vo oo w o o cooo t--v£) u-1 r~- o rl >-• to to ri r^ ro •
O M w MUMWliliMii MM iiiiniiclc4 clMCiclCOto^*^^ ^ V© O 00 C\ •
I I I 1 I 1 1 I 1 II I 1 1 I I 1 I
I 1 I I I I I I II I I
I I
oo O M t^ O\oo in t-s.
__ c« ro en <4- m CT\ ^\o
•^ M ■«J- u-i m
+I+I+I+I+I+I+I+1
Oiomr»<^NHO
« >-" (I c» N -"i- r^oo
'-' H N t<
Mil
§
+++
00 O xvooovo u-irl
M « « 00 t-^ O O
VO tJ- moo VO M M lr»
O H '1-On>-iOO r~.r»i
i-imi-imOCTs>-iN
iH •-> rl r<
++++++++
t^ to fov£> oo r< >o t^
VO 00 0\ r> i-i r^vo c?\
I M VO "1 rl c^
++++++++
m ■^ ^^ "^co Looo
II 11 I I II
ro r^ Ti- ro ovvo ^vo
1-1 IH M o\ 1-^ o o
;5 „ •- f< ^
« E^ H* H H
p o .2 ." .™
._, sj ~ ^ jg Jg
pC c3 •-;•—'-::: tti v>-. u^ ui
&i'C o 3 O O O O O
3 »:; -s o >>^ rs 72 rS
of Chromatic Dispersion.
\77
^ to vooo OO O too CN rl lo ro to vooo O i- O - O ^ voM oo vn c~>
to ON to « q j-vo vot^tot-^coo »nM rt t^Noo rt vovo &o oo oo o
O to Mr, ^vo ^ CO to n ^h vn U-, t^vo 00 ^l-vo t^^ t^«
+ +I I + + +I +++ I I I + 1
I I +
^ ''^^ f^J,' "'I-'^OVOVO >o t-,00 0> w O t^ t< 00 VO cvoo >-. oo «
M t-^ vovo -J-vo t~-toM00NM VO civovoovco to r« ^
I I I I I I I I I I I I I 4- 1 I I I I I M + I I I
to ov to On t}- w "i-oo 00 t^-TJ-M o too t) O Ov'^h'd-O toCvt^O »*.
tOM lO'^voii M rhroaN>-i H totow r^tow t-^oo t^ to vo to to X
t-^00 r^ to to to to ^
+ + + ++ I + I + + + + + + I + + + + + I I + + + +
Ovvo 0>-'OvOOvotoCTvr--oooo ■»!•'-' t^totopirJt^cNTt-.r<.r«
M iit^M lOtOtOHHt^W Wl-lt^tOt~NtO tJ-OO •^ w
+ I+++I 1++++++ +4- I I I + I I I I I +
tot^rloo ONt^rlvoOO totOrl-OvM t^ -^vo Ovrlvo too rt too to
^tO>-ltltltOr)tOtOtO«tO>-iVOclvo Cl'-'QVOCNtOtJtOM
O 11 M IH M „
llllll + llillll-fl + llllll +++
CO (^ to iH t^ to to vovo f^tototori r-^^J-in tOT^-t^r^toroON tovo
g>i i-i >-iN Mr»t<'<l-i->rt to toiHVOii'a- CO ?i
+ + + I + I ++ I I I I I +++.+ + II I + I II +
+ I I + + + I I I ++ 1 ++ I ++ 1 + + + + + + + +
«0 rSi'-'toNtOrj
g ji^ 2 >r, ;c i?;
':-T3 0 ^ „- <U ^-v- O g o
—' to rt « -3 rt •= ff C . s
fe til sJ t^ t^" &: &: t,* Sh' i^ ci d d si lii d cj d cj ci si cC cJ Gh"
378
Mr. M. Ponton on certain Laws
•rf->«nro-*-J-M«r«vOf»r»oor^ t-^vO O^ "4- t-^00 vo vo •^ "i Osoo 0\ O
O
i
3
tn
o
b
ro ro r< c^io c< 0 O locc t-^io ro 0 f^ d ro 0 Ovo 0 O C^ H r) O meo
t^ U100 C^ -< 0\ tJ- C\oo •- MCTsrJ O'Ooo r< r> 0\0 Cn "^ M O t-~- ovo N
.
0 MM MM« M MNcJrtMt^t^r^ •<i-oo 00 u^
i*
O
O
b
+ + + + + +++ + +++++ 1 +++ + + + + + + + + 1 1
O t^>^H r--M t^ Or^fJ t~-N t-vo OM» HiOf^OO'-'i^t^'^N r^vo
e^MC^c*'d*^^l'^r^ i^vo Cs-^^^t^ploo m^ m\o r^i^ri-M u-ti-riu-iro
O M Mi-ii-i«MMi-iNr>iHrrit<Mro rj-vo "i w •<J- c^so ^O
d
O
O
4
p
? 1 1 1 i 1 1 1 1 1 1 1 ++ 1 1 1 1 1 + 1 1 ++ 1 1 ++
O H tl t< -^M MOO mT^vno^^oO i/-,m 0<fi^ •& u~,\o 00 r~ m m vo r<
M f) to vO M invO M vOU-iMM'^t^MOOOO'l- CwO u-^ m •<}- tJ-vO CO
HI d^M MM rttlMt^rJ
i
o
8
b
4-++ 1 +++ 1 + 1 1 +++ + + 1 1 1 + 1 1 1 + 1 +++-
toly^H MVO c) M r^to0\0 COt^H -^OnO C^<J^O O "^vnCvO^ t^^O
MM cot^•<i-t^Mcno^O^^^O^O t^t^iy-iuiMMMr-.vioMOO'oto
O M M MM M MMM'^'^VOm
K
o
o
A
o
b
++I+I 1 1 1 1+++1 1+1 1+1 1 I++I++1 1
00 to ooo osMtoovotnUMOtlt^O r~-vO too t^f^'+Mvo M r^t^
M t--oo "^ M \0 •* Tj- N too to^vnvocJ tO'^u-i <i-vo -d-vo tovo u-ivo
M MMMf(t»C«Mt4MM U^tO MVO
Q
o
o
i
o
b
+111111+1111111 ++l+i+lll+lM
O ^d vrf^^r^totoTj-toTi-ooo ■^to t^\o t^totot< m tj-o m ly^^J-tl
MOO^^"^O^^M^o•<l- •q-o t^ m c^o mio m cvi^moo o m ■^oo to
OmM M M M MM-^t^MMVO MVO
O
O
o
b
+ 1 ++ 1 1 + 1 1 + 1 1 +++++ 1 + 1 1 1 1 +++ + 1
O t^ O M VO Cs M ■^^o t^M 0\0 tot* ©Ntivo CNintoO ff\vnu-vM t^o
0\0 ro-^u-iO t« t<00 w^mr-ONt^vO'* to\0 Ooo •"(-^•■i-M rt o 'J-m
OM M MMMtOMMfjMtOlOt^U-l
n
O
O
■ A
O
b
++ 1 1 +++++ 1 ++++ 1 I 1 + i ++++ t ++++
^n' ':
: :
i> ■
J:o :
— :
.5 „" • • '•
: s
,
0* 0
"w
"5 ^._ • • •
>-,
2
Ti-
M O
-^ ^
ca
■ o z.' — ; :
u
■S-t: • M • !3 J r) -
'5
:E 5 . . != '3
^ ^ u 5 o (s
u
2
ii !S 50 , • J; "S ~ • .
M*- u-, - S « - - -
V
^
5 -^ Z^Z-^t?.-32^ ■^•111 S^ 5:15^-3 §iJ Z g g
■= ^. 11 i 1 •= 2 "^ ■€ •= ■= o 2 .2 ^^ m ^ S =3 i -2 ^ "o "S
'C'^c^zc«2Zc«o^SScmSc«f5iid^ — ?^dc«S;z;cc
iIa;a;s^£^a;a;e^tp^a^ei^ciJp^c^CL;pL;eke,'p^PL;s^a;&,'p^ek(i^cu
pi-
& .
«!2
d i
c i
XT-
xr-l
1
O
O
•
o
sk
o
O
(-^ r-~ to t-~vo m
+
Vn •5j- ^ M M ON .
•* to to t« t< t< • '
o :
o :
Sm
o
1 P
1
0
(
to ^i- t^ to tJ- u-i ir
•5^ U-) ly^oo OO O "■
M M M M M M t»
?
o
i c«
o
o
1
o
1
O 0 0 o O 0 o
o o o o o o o
\D W, \r\ ri- Tj- tJ^ t*
o
o
O
1
0 o o o o o o
o o o o o o o
1
f, „ t« M M M M
o
1 a
o
i
o
o
1
+++++++
1
O 0 O O O 0 o
o o o o o o o
rt M M M t< M M
o
o
1 s.
o
? 1 1 II 1 1
1
0 0 0 0 o o
o o o o 0 o ;
t* H M M M tl .
Q
o
o :
1 s.
o
? 1 1 1 1 I
ooo o
ooo . . o .
OMM ■ . M •
O
o : : ;
o ...
i.
o ...
o
1 + 1
• to
o
JZ '^
d
a 6
s
■Z § c Z -S
es
a- ^ X — r- " "
a o tj c a = £
a
■vJdZ '53 - bcZ -
f^
= C~.2 = C^
^ ii S ^ S ^ O
o ci c — c a ..^
O^OwO^O
^ Pe; Ps,' ^ b* C^; fi
of ChromaticDispersion.
379
VO o •+ t^oo
VO
►< C\>3
OO O t^ r^
M
CO CO r-~
r^ to M M
«
woo
ThrotOTj-c* H roH 11 to«
c>\ ro r^ ovoo r^>o vo o>
11 " O CvvO vo N O . VO
vo On N vn r»N CO vrioo O ►< O >" O ■^ moo OOONOfO'l-t^ONHroooi-irl^ rooo O r-mO t^iioooooo f~c< vo
nro^'i-ioi-' w ►• H H copnw w-ivo to t*N r<i ^ ^ ^ ^ vovo no r^ t^ t^ t^ t^OO OnO O « Nno OnOnw i-" uiuit^.
M>1MMI-lltMC4C<HmrO
000000000000000000000000000 oooooooocooooooo
ooooooooooooooooooooooooooo
00 t^OO OnOO '^ "O m ^>0 vr> CO ^ «^ tooo H i-< ion© in O '^no m no «o
0000000000000000
00 00 11 NO t^oo o
O O -^ NO
00000000000
00000000000
000000000000
000000000000
H NOVO O t<
»-• to c< CO l-l w
000000000
000000000
+++++ I + I +++
I +++++ I H-1++1 1+ I + ++I++I I++
00000000000000000000
il-ntotoco'-'HwwcotOrtH'iH tONO tJ- o\ r»
00000
00000000000000000000 .00000
tJ- CO c< to to
0000000000000
OOOOOOGOOOOOO
«N0«*-tOWf1C<t<0MlO^t^
I I I I I I I + I I I I I I I I I I I I I I I I I
+ IIII + III + II+ II
0000000000
0000000000
i-i>-iMtor)i-''-i'-''ii-'
00000
00000
0000
0000
to ^^ •-• f-"
000
000
11 cl 10
00000
00000
000000
000000
•<}-H'<l-Ht^ •t^tonc^'l-c*
1 1 I I I + I + 1 I
+ I III + 1IIII+ III +I + II ll + lll
0000000
0000000
000000000000
000000000000
M to >4- t^OO C< ^ P~ ll CO <4- >H
I I
++++I1 I +11+11+ +++1+1111+11+1
M to rl to r>
66600
rt On r»
O toJS
fao
a es
V u
« ea 91 y 2 ^ ^ r_- cJ
•SNJtodi-i-rt-?^
fen ■•-* N . ^ tn " to^ ^^ **"• ^ JZ ^
^ ?; ^ z 2 '
eo en w CO « 'l
ed ed c4 etf eij <
'5)'S3 to'Sj'fcb ,
- o
4) "S
2 <*- "c S
4) O 'o eS
« « '^ o
E^-5^
■ - a c
"o'E
?i: c,
^ 5 ='
^ --^ ^ ^ '^ ^» r^ ^
- c< O
-> " 5 5 o - •-
I c3 ' ■■- f^ rt c3
: "^ "= "o ^s 'i 'i
I Nil • — C3 ♦; Ni-l <*H
= "^'^ 2 ° ®
i S is 0 O
.? r: o = .ti = :::
l^p;^pi^^Cbp^;xp:ip:wdpidp^^;^PHP^o^cCPK'i:i^'pH'&^cucC&JpH'a,'cJPHCu04HU^ii^
[ 380 ]
LI. Chemicnl Notices from Foreign Journals. By E. Atkin-
son, Ph.D., F.C.S., Teacher of Plnjsical Science in Cheltenham
College.
[Continued from ]i. 2^'] .]
^EBRAY has described* some methods for obtaining a
number of artificial phosphates and arseniatcs, many of
them identical in form and composition with known minerals.
AVhen an insoluble carbonate is treated with excess of aqueous
phosphoric acid, or arsenic acid, the carbonate is usually changed
into a crystallized phosphate or arseniate. The proportion of
water of liydration varies with the temperature. With phos-
phoric acid and carbonate of lime, a phosphate of lime is ob-
tained of the composition P0^2CaO, H0 + 4H0. At a tem-
perature of 100° the phosphate PO^, 2CaO, HO is obtained.
Arsenic acid and carbonate of lime at the ordinary tempera-
ture give the body AsO^, 2CaO, 4 IIO, which is the mineral
Haidingerite.
In a similar manner the following bodies have been obtained : —
At 70° phosphate of zinc . . . PO^, 3ZnO, 4 HO
„ 250° (in a sealed tube) . . . PO^ 3ZnO, HO
„ 70° phosphate of copper . . P0•^ 3CuO, 3H0
„ 70° arseniate of copper . . AsO^, 2CuO, 110, 3H0
„ 70° phosphate of manganese VO^, 3MnO, 4 HO.
By acting on the insoluble phosphates of lime, magnesia, &c.
wdth a metallic nitrate or sulphate, crystallized compounds are
obtained, the composition of which varies with the temperature.
At 70° phosphate of lime, PO', 2CaO, HO, and arseniate of lime,
AsO'^, 2CaO, HO, give with nitrate of copper the ])liosphate
P0^3CuO, 3H0, and the arseniate AsO^ 3CuO, 4H0 ; and
at a temperature a little above 100° C,
The phosphate of copper, PO^ 4CuO, HO (libethenite);
The arseniate of copper, AsO'^, 4CuO, HO (olivenite).
These latter bodies, which have the form as well as the com-
position of the native minerals, are better obtained when the
reaction is effected in a sealed tube at 140° — -150°.
At high temperatures (250° — 270°) water transforms certain
phosphates and arseniates into other well-crystalhzcd species.
Blue phosphate of copper, PO^, 3CuO, 3H0, is transformed
into magnificent crystals of libethcnite ; and arseniate of copper,
AsO^, 3CuO, 4 HO, is changed into olivenite.
Crystallized double jdiosphates are obtained by mixing the
solutions of acid phosphates with metallic solutions. A solution
of acid phos])hate of lime, mixed with a solution of nitrate of
* Bulletin de la Societe Chiinique, p. 13-1.
M. Chauccl on the determination of Phosphoric Acid. 381
urauium, ^xMs chalcolite, P0\ 2CuO + PO-^ (Ur^ 03)4 + 16110,
or double phosphate of copper and uranium.
Chancel proposes* the following method of separating and
estimating phosphoric acid in the presence of bases : it depends
on the insolubility of phosphate of silver, 3 AgO, FO^, in a neutral
liquid.
The substance taken is dissolved in the least quantity of dilute
nitric acid, and the solution diluted with water. The clear
liquid is mixed with a sufficient quantity of nitrate of silver,
and then Mith a slight excess of carbonate of silver. This opera-
tion must be performed in the cold when the liquid contains
any substance, such as manganese, which is precipitated bv the
application of heat.
The phosphoric acid soon separates as yellow phosphate of
silver ; the precipitation is complete when the liquid no longer
reddens blue litmus paper; the precipitate is then filtered, care-
fully washed, introduced into a flask, and dissolved in nitric
acid. The silver is now precipitated by means of hydrochloric
acid and the filtered liquid supersaturated with ammonia, and
the ammoniacal phosphate precipitated with sulphate of mac:-
nesia in the ordinary manner.
The advantages which silver salts have in this separation of
phosphoric acid, consist greatly in the readiness with which the
silver is removed from the solution ; but they have the great
disadvantage that, when the phosphoric acid is in combination
with alumina, oxide of iron or chrome, it is not separated from
these bodies, but merely precipitated with them. The use of
bismuth compounds which Chancel proposesf is not amenable to
these objections ; it furnishes an exact and easy method, one
susceptible of the widest application.
The method depends on the insolubility of phosphate of
bismuth in liquids which contain even a considerable propor-
tion of free nitric acid. The acid nitrate of bismuth is pre-
pared by dissolving one part of pure subnitrate of bismuth
(BiO-^, >s'0'^ + Aq) in four parts of nitric acid of sp. gr. 1-36.,
and adding to the solution thirty parts of water. Thus prepared,
the solution is not made turbid either by boiling or by the
addition of any quantity of water. The substance to be de-
termined is dissolved in distilled water; if necessary a small
quantity of nitric acid is added, care being taken to avoid excess,
and the solution diluted with water. If the solution contains
sulphates or chlorides they must be removed, the former by
adding nitrate of baryta, and the latter by nitrate of silver. The
solution of acid nitrate of bismuth is then added, as long as a
* Comptes Rendus, December IS59. f Ibid. February 27, 1860.
382 M. Scheerer on the determination of Magnesia.
precipitate is formed. The precipitate which separates is of a
beautiful white, is very dense, and settles readily, more especially
when warmed ; the whole liquid is heated to boiling, filtered and
washed with boiling water. It is then dried and heated. It
has the composition BiO^, PO^, which is that of a neutral phos-
phate, for bismuth is triatomic, and replaces three atoms of water
in tribasic phosphoric acid.
Pyrophosphoric acid is also precipitated by acid nitrate of
bismuth as neutral pyrophosphate of bismuth, 2BiO^, 3/>P0'^*.
The precipitate is white, but much more voluminous than with
tribasic phosphoric acid. Metaphosphoric acid is likewise pre-
cipitated by nitrate of bismuth. Both these precipitates, however,
are converted into the tribasic phosphate of bismuth when boiled
with excess of the bismuth solution; the metaphosphate requires
a somewhat more prolonged ebullition. It is therefore of little
importance in what modification the phosphoric acid exists in
the solution to be determined.
This method affords a very delicate means of determining
phosphoric acid. Chancel was able to determine and separate a
milligramme of phosphoric acid in the presence of 120 milli-
grammes of alumina ; and the precipitation is so rapid that it
will be possible to estimate phosphoric acid by means of a
standard solution of acid nitrate of bismuth.
To estimate magnesia in the presence of the alkalies, Scheerer f
proceeds as follows : —
The mixture of magnesia and the alkalies being given, is con-
verted into neutral sulphates and weighed. This mass is dis-
solved in a small quantity of water, and the solution divided
into two parts of known weight. In the one the magnesia is
determined by the addition of phosphate of soda, and in the
other the potass is precipitated by bichloride of platinum. The
soda is estimated from the difference.
According to Rose J, when silica of the density 2*2 is mixed
with fluoride of ammonium and the mixture heated, the silica is
completely volatilized as fluoride of silicon. With quartz and
sand the action is less energetic. Rose recommends the use of
fluoride of ammonium as convenient for decomposing silicates.
It may readily be prepared by adding ammonia in excess to the
commercial acid, and then a little carbonate and sulphide of
ammonium. The liquid is allowed to stand, the clear liquid
* Chancel represents ordinary or tribasic phosphoric acid as PO", bibaaic
phosphoric or pyrophosphoric acid as p^O', and monobasic or meta-
phosphoric acid as mPO'.
\ Liebig's Annalen, November 1859.
+ PoggendorfF's Annalen^ September 1859.
M. Bechamp on the Preparation of Permanganate of Potash. 383
decanted and evaporated to dryness in a platinum crucible ; a
small quantity of carbonate of ammonia is added occasionally
during the evaporation, and when the mass becomes pasty, it is
stin-ed with a platinum spatula. The dried salt may be kept in
vessels of platinum, silver, or gutta percha.
In order to decompose a sihcate, it is mixed in a state of fine
powder with six times its weight of fluoride of ammonium, a
small quantity of water added, and the mixture heated at first
gently, and gradually^to redness as long as vapours are given off".
Usually one operation is sufficient ; the residue is treated with
sulphuric acid, and the excess of this acid cb'iven off. AVhere
the sulphates formed do not completely dissolve in water con-
taining a little hydrochloric acid but leave a residue, the inso-
luble part is again treated with fluoride of ammonium.
The temperature must not be raised too high in the operation ;
for if the silicate contained alumina a fluoride of aluminum
might be formed, difficult to be decomposed by sulphuric acid.
Hyposulphite of soda, according to Lowe*, dissolves sulphate
of lead, which may in this way be separated from sulphate of
baryta. A concentrated solution of hyposulphite is poured on
the mixture of the two salts, and the whole digested between
15° and 20°. At a higher temperature a sulphide of lead inso-
luble in hyposulphite of soda might be formed. The residual
sulphate of baryta carefully washed is weighed, and as a control
the lead in the hyposulphite may also be determined.
For the preparation of permanganate of potash, Bechamp f
recommends the following method. In an iron basin ten parts
of powdered binoxide of manganese are mixed with twelve parts
of fused caustic potash ; a little water is added to the mixture,
which is rapidly dried, and introduced while still hot into a tubu-
lated stoneware retort, and a current of pure dry oxygen passed
into it. To the neck of the retort a tube is fitted just dipping
ander mercury. The absorption of oxygen is very rapid; it is
complete when it bubbles through the mercury. The cooled
mass is then exhausted with hot water, and a current of carbonic
acid passed through the solution, by which the manganate is
transformed into permanganate. When the solution has the
characteristic colour of the permanganate the current of gas is
stopped, the oxides of manganese are allowed to settle, the clear
solution rapidly evaporated and allowed to crystallize ; the mother-
liquors yield a further crop of crystals. In general a pound of
binoxide gives five to six ounces of permanganate at the first
crystallization.
* Journal fiir Praktische Chemie, vol. Ixxvii. \^. 7^-
t Aniiales lie C/iiinie et tie Physique, November 1859.
38'1« M. Lautemanu on the Formation of Propionic Acid.
Lactic acid is regarded by Kolbe as oxypropionic acid, that is,
as proj)ionic acid in which an atom of hydrogen in the radical is
rc])laced by peroxide of hydrogen, just as chloropropionic acid is
propionic acid containing an atom of chlorine in the place of an
atom of hydrogen.
c« H^ on Q.2 C6 H^ CI on 02 C6 H-^ (HO^) on ^^
Propionic acid. Chloropropionic acid. Oxypropionic acid.
In accordance with this view it might be expected that if hydro-
gen could be directly substituted for the group HO^, propionic
acid would be regenerated, and this mode of regarding lactic acid
would receive additional support. Lautemann* has made a
series of experiments in this direction.
The change is not eflfected by treating lactic acid with sodium,
or with sodium amalgam, nor with electrolytic hydrogen ; but
it takes place by means of hydriodic acid. When lactic acid was
saturated with hydriodic acid gas, a separation of iodine com-
menced almost immediately; to complete the change, the solu-
tion was heated in a closed tube to 140°. The contents of the
tube were then distilled with sulphuric aeid ; the distillate, which
contained hydriodic acid and free iodine, was treated with car-
bonate of silver, and filtered. On cooling, crystals separated
which had the appearance and all the properties of propionate
of silver. The change is thus expressed :
C6H6 06+2HI = C«H6 0H2HO+2I
Lactic acid. Propionic acid.
Regarding alanine as amidopropiouicacid, C^ H'^ (NH^)0^\p>2
or propionic acid in which an atom of hydrogen in the radical is
replaced by the group NH'^, a view rendered highly probable by
the investigations of Perkins, Cahours and Ulrich, and regard-
ing lactic acid as oxypropionic acid, — it is obvious to expect
that lactic acid maybe transformed into alanine, as Strecker has
shown that alanine may be transformed into lactic acid. Kolbe f
has effected this in the following manner : — By treatment with
pentachloride of phosphorus, lactic acid is changed into chloride
of chloropropionyle ; by treating this with absolute alcohol, it is
changed into chloropropionic ether. This is then heated with
ammonia in a closed vessel to 100^, the contents of the vessel
evaporated and exhausted with absolute alcohol, by which the
greater part of the chloride of ammonium is left undissolved. It
is then boiled with water to expel the alcohol, and subsequently
with oxide of lead, which decomposes the rest of the chloride of
ammonium, forming with the chlorine a basic chloride of lead,
* Liebig's Annalen, February 1860. f Ibid.
M. Lautemann on the Preparation of Lactic Acid. 385
while the ammonia is liberated as gas. The mixture is then
filtered, saturated with sulj)hurctted hydrogen, filtered and
evaporated ; on coolinir, alanine is obtained in beautiful crystals.
C^H^C10=|o^^2XH3+oHO = t»HnNH')OnoHCqi»OHNII^C.
„, , . . -^ .1 • • -^ Alcohol. Chloride c
Chloropropiouic Amidopropiouic ammoniun-
ether. acul.
According to Lautemann*, the following is an advantageous
modification of Bensch's method of preparing lactic acid. The
proportions of sugar, tartaric acid, milk, and cheese are the same;
but instead of chalk an equivalent quantity of oxide of zinc (com-
mercial zinc-white) is employed. The temperature must be
between 40 — 50^; the fermentation is complete in eight or ten
days. The whole mixture is boiled in a copper vessel, filtered,
evaporated, again filtered, and allowed to stand. On cooling, pure
lactate of zinc separates. To obtain the free acid the lactate
is dissolved in boiling water, the zinc separated by sulphuretted
hydrogen, filtered and concentrated. This solution contains man-
nite and lactic acid; to separate the two it is agitated with ether,
which dissolves the lactic acid, and leaves the mannite. On eva-
porating the etherial solution the lactic acid is left behind.
Kekule foundf that chloracetate of potass, when heated iu'
the presence of water, is decomposed with the assimilation of
two equivalents of water, fonning chloride of potassium and
glycolic acid : —
C W CI K 0"* + 2 HO = KCl + C-i H-* 0«.
Chloracetate of Glvcolic
potass. acid.
Heinz has found % that when the same salt is heated in
methylic alcohol, or, still better, when free chloracetic acid is
treated with methylate of soda, chloride of sodium and a new
acid are formed : —
C^H3C10^+C2H3Na0-2 = NaCl + C«H6 0«.
Chloracetic ^lethylate New acid,
acid. of soda.
This experiment was undertaken iu the expectation of forming
lactic acid. The new acid is, however, isomeric, and not iden-
tical with lactic acid. The reaction is capable of great extension ;
by acting on the homologues of methylic alcohol^ a series of new
acids is obtained corresponding to the higher members of the
lactic acid series.
* Liebig's AnnaJen, Februan,- 18G0.
t Phil. M.i<^. vol. xvi. p. 138.
X Pojrgendorffs Annalen, Feb. 1 8(10.
386 M. Heinz on two New Series of Acids.
The monocliloracetic acid was prepared by Hoffmann's method,
which was found very convenient. A quantity of sodium was
then dissolved in anhydrous methyhc alcohol, and a correspond-
ing quantity of chloracctic acid added. The action was very
energetic, each addition of the acid being attended with a hissing
sound. When the action was complete, the mixture was heated
for some hours to a temperature of 100° ; the alcohol was then di-
stilled off, hydrochloric acid added in slight excess, the mixture
rendered feebly alkaline with soda, and evaporated to dryness.
This mass was exhausted with alcohol, the alcohol distilled off,
and the aqueous solution of the residue mixed with sulphate
of zinc and evaporated to dryness. On treating this mass with
alcohol a zinc-salt was dissolved out, which was deposited from
the alcoholic solution in large, colourless, acute rhombic octa-
hedra. The analyses gave for the formula of this salt, dried in
the air, C^ H^ Zn06 + 2HO : the water is given off at 100° C.
To obtain the free acid from this salt, it was dissolved in water,
the solution saturated with sulphuretted hydrogen, and filtered
from the sulphide of zinc ; on evaporating the filtrate, acid
vapours were given off; it was accordingly distilled. The tempe-
rature gradually rose to 198°, at which point it remained con-
stant. What now passed over consisted of the free acid, which
is a colourless viscid liquid of the sp. gr. 1'18. It has an
acid, but not unpleasant taste; its boiling-point is 198°; it is
very soluble in water, and readily attracts moisture from the
atmosphere. It burns, when it is inflamed, with a blue non-fuli-
ginous flame. By saturating the acid with carbonate of zinc,
filtering and evaporating, a zinc-salt was obtained identical with
that obtained at first.
The acid, though isomeric with lactic acid, differs widely from
it, and also from sarcolactic acid. The new acid is volatile ; its
zinc-salt crystallizes readily in large crystals, and is very soluble.
Its potash and baryta salts readily crystallize ; its lime-salt does
not crystallize, and is easily soluble in water; and lastly, the
silver salt melts at 100°, and does not fuse. In all these points
there is a wide difference from the corresponding compounds of
the lactic acids.
The acid is derived from glycolic acid by the substitution of
methyle. Glycolic acid is bibasic, and, according to Socoloff and
Strecker, contains two atoms of replaceable hydrogen, one of
which is more readily replaced by a metal, and the other by an
acid radical. If this acid were glycolic acid in which the basic
hydrogen is replaced by methyle, it would have a constitution
analogous to that of the ordinary ethers ; it would be, in fact, a
glycolate of methyle, and would yield, when treated with an
alkali, an alkaline glycolate and free methylic alcohol. But
M. Heinz on two New Series of Acids. 387
Heinz found that, when treated with caustic soda, it yielded a
soda salt which was not glycolate of soda. Another supposition
is that it is glycolic acid in which the atom of hydrogen more
readily replaced by an acid radical is replaced bymethyle; on which
view its constitution would be represented thus, C^'H^O^l /-x4
Heinz found that the acid, when treated with benzoic acid, did
not form benzoglycolic acid, as might have been expected on
this view.
Heinz considers that the acid is oxacetic acid (glycolic acid)
in which an atom of methyle is contained in the radical. He
writes the formula thus, C^H^O''"! ^g i i. jl
' H f ' ^ names it metnox-
acetic acid to express this mode of deriving it. The homologous
acids, formed by the same reaction, receive the names ethoxacetic
acid, amoxacetic acid, &c.
Heinz has described several of the salts. Methoxacetate of
ammonia forms a mass of radiating crystals which are very
deliquescent. Methoxacetate of baryta, BaO C^ H^ 0^, forms
colourless, transparent, prismatic crystals, readily soluble in
water, but difficultly so in alcohol. Methoxacetate of copper,
CuO C^"H^0^ + 2H0, forms bluish-green, transparent, acute
rhombic prisms with good reflecting surfaces. They are per-
fectly soluble in water, but little so in alcohol. Methoxacetate
of lime forms a syrupy solution which does not crystallize ; but if
evaporated over sulphuric acid, it dries up to a solid mass,
which gradually becomes crystalline. Methoxacetate of potash,
KO C^'JP0^ + 8H0, forms large colourless transparent prisms
permanent in the air. They are readily soluble in alcohol. On
the addition of ether to this solution, a salt of the formula
K0C^H^0^ + 6H0 is precipitated. Methoxacetate of lead,
PbO C^ H^ 0^, forms a solid, white, crystalline mass like Wavel-
lite. Methoxacetate of silver, AgO C^ U^ 0^, forms fine needles,
which are somewhat soluble in cold and readily so in hot water.
Elho..cctic acid, C»H»0«=C»H'a^^O, i^„^^^i„^j .^ ^
similar manner to methoxacetic acid. It boils at about 190° C,
The baryta salt is very readily soluble in alcohol and ether.
Dissolved in water and evaporated, it forms a syrupy solution,
which crystallizes, after some time, in small needles.
A.,oxacetic acid, C'^ H» 0« =C» H'" 0^ q.^ ;^ ^i^i,^^,^
obtained by the action of chloracetic acid on amylate of soda.
A solution of its zinc-salt in dilute alcohol is decomposed by
sulphuretted hydrogen and distilled. At first alcohol and water
pass over, and then the acid at a temperature of about 235 —
388 Niemann on the Action of Ethylene on Chloride of Sulphur.
240° C. It forms a yellowish-green liquid, somewhat insoluble
in water, but miscible in every proportion with alcohol and ether.
Heated in a platinum spoon it takes lire, and burns with a clear
flame.
Neither the zinc nor the baryta salts crystallize. The potash
salt crystallizes in a wavellitc-like mass. The copper salt forms
microscopic blue needles.
By the action of chloraceticacid on the soda compound of phe-
nylic acid, Heinz obtained a new acid, phenoxacetic acid,
C'2 H^ NaO^ + C* IP C104 = NaCl + C""^ IP 0«.
Phenylate Chloracetic New acid,
of soda. acid.
The new acid is isomeric with the next higher homologue of
salicylic acid, C^"* H^ 0^", or, as is more probable, with Gerland's
oxybenzoic acid.
Phenoxacetate of baryta, C'^IFBaO^ + 3110, is obtained by sa-
turating the free acid with baryta water. It crystallizes in very
large, thin laminse. Phenoxacetate of copper, C'^^H^ CuO^ + 3 HO,
forms small tabular or prismatic cferulean crystals, which are
very little soluble in water. Phenoxacetate of lead forms small
microscopic granules. Phenoxacetate of silver, C^^ H'' AgO^, forms
small, flat prismatic crystals, which are frequently arranged in
groups.
Phenoxacetic acid, Q'^ H^ 0^ = C^^ H^ 0^ ne ti, ^ •^
' TT r-0\ The free acid
may be obtained from any of its soluble salts by the addition of
a strong mineral acid. According as the decomposition is
effected in the warm or in the cold, the acid is precipitated as
an oil, or as an amorphous powder, which by agitation becomes
crystalline. In the temperature of the water-bath it gradually
disappears.
The brown liquid produced by the direct action of chlorine on
sulphur has been found by Carius to be a mixture of subchloride
of sulphur, S^ CI, with bichloride of sulphur, S C1-. Niemann *
has tried the action of ethylene gas on this body. When the
dried gas was passed into the chloride, it was rapidly absorbed
with disengagement of heat, and the colour changed from a
brown to that of the pure bichloride. When this change of
colour was complete, the absorption ceased; for ethylene gas has
no action on bichloride of sulphur. The product was then treated
with dilute soda ley, by which sulphur was deposited. A large
quantity of water was added, and the whole submitted to distil-
lation. A yellowish oil passed over, which was washed with water,
and dried over chloride of calcium. It seemed to boil at about
* Liebig's Annalen, March 1860.
MM. Busseuius and Eisenstiick oji Petrol. 389
190 — 200°, but could not be distilled without decomposition,
and its purification was therefore very difficult. It is insoluble in
water, but is partially soluble in alcohol and in ether. Its alco-
holic solution yields a precipitate with chloride of gold, and with
protonitrate and pernitrate of mercury.
The most peculiar property of this oil, is that of causing a
painful burn when it comes in contact with the hand, which
heals with difficulty. The substance analysed was evidently not
quite pure; but the results obtained agree best with the formula
C"* H** CIS^, which would represent a bisulphide of chlorinated
ethyle.
Bussenius and Eisenstiick* have investigated a rock oil which
is obtained from some lias shales near Hanover. The crude oil is
distilled with high-pressure steam, and the oil which distils over
is treated w'ith sulphuric acid, which removes from it a pecuhar
bituminous smell. Thus purified it comes into commerce;
but the oil for this investigation Bussenius and Eisenstiick
took as it distils over with the steam, dried it, and submitted
it to fractional distillation. It began to boil at 135°, and the
temperature gradually rose to 270°. The distillate below 180°
was further examined. It was found to be composed mostly of
hydrocarbons of the general formula C„H,„ and apparently
ranging from C'^H^^to C^^H^^. Notwithstanding very great
labour, it was not found possible to isolate these ; nor were the
attempts to procure definite compounds from them more suc-
cessful.
Besides these hydrocarbons, the oil contained a new hydro-
carbon, which the authors name petrol, which, however, they
were not able to separate directly ; but when the oil was treated
with a mixture of sulphuric and nitric acids, a crystalline
nitro-compouud of this body was produced : the other hydro-
carbons, of which the oil is mostly composed, are not altered even
by prolonged contact with this acid mixture. This nitro-com-
pound was purified by repeated crystallizations from alcohol. The
analyses of the substance gave for it the formula C^^ H" (NO'*)^,
that of the hydrocarbon from which it is derived being C'^" H'*^.
The body was not quite pure, but probably contained some of
the nitro-compound of a higher hydrocarbon, C'^ H'^
Trmitropetrol crystallizes in large long needles ; it sublimes
at 175°. It is not soluble in water, and but slightly so in ether-
alcohol, or in benzoic; but it dissolves in about 16 parts of boil-
ing alcohol. AVhen it is treated with alcohol it is converted into
* Liebig's Annalen, Februarv ISfiO.
Phil Mag. S. 4. Vol. 1 9. No. 128. 3% 18C0. 2 D
390 M. Liebig on the Formation of Tartaric Acid from Milk-sugar.
nitropetroUdiamine, C^^ H^ ' N^ O'* = N^ ^ H^ , a basic sub-
stance which crystallizes on slowly cooling from an alcoholic
solution in large orange-coloured prisms. This body forms cry-
stalline salts with sulphuric and hydrochloric acids. When it
is treated with iodide of ethyle, it forms a compound in which
three of hydrogen are replaced by ethyle — triethylnitropetrol-
fCi6H7(NO'*)
diamine, N2^ (C^ H^)2
Petrol has the same composition as xylole (Cahours, Church),
but, judging from the nature of its derivatives, it does not appear
to be identical with it.
Liebig gives a detailed description* of the formation of tartaric
acid by the oxidation of milk-sugar by nitric acid. He discusses
the mode of occurrence and constitution of tartaric acid, and
several allied vegetable acids, and mentions an experiment in
which he tried the action of aldehyde on cyanogen dissolved in
water in the expectation of efiecting the synthesis of malic
acid. It gave, however, an unexpected result. A flask contain-
ing about two quarts of water was saturated with cyanogen,
about an ounce of aldehyde added, and the whole left in a
cool place. The fluid remained clear and colourless; but gradually
a mass of white crusts separated at the bottom of the flask,which
were found to be oxamide. The liquid, saturated for a second
and third time with cyanogen, yielded fresh quantities of oxa-
mide. On distilling the liquid some more oxamide separated,
and it appeared as if the aldehyde had formed a combination
with oxamide which was decomposed by boiling. The aldehyde
which distilled over contained some acroleine. The mother-liquor
from which the oxamide had deposited contained oxalate of
ammonia.
The aldehyde in this experiment, either by its mere presence
or by its cooperation, promotes the combination of cyanogen with
water, to form, according as it combines with two or four equiva-
lents of water, oxamide or oxalate of ammonia. The aldehyde
acts as a sort of ferment; while any other affinity of the cyanogen,
for the hydrogen or for the oxygen of the water, appears to be
quite suppressed.
* Liebig's Annalen, January and February 1860.
[ 391 ]
LII. Proceedings of Learned Societies,
ROYAL SOCIETY.
[Continued from p. 317.]
November 24, 1859. — Major- General Sabine, R.A., Treasurer and
V.P., in the Chair.
npiIE following communication was read : —
-*- " On Recent Theories and Experiments regarding Ice at or
near its Melting-point." By Professor James Thomson, Queen's
College, Belfast.
My object in the following paper is to discuss briefly the bearings
of some of the leading theories of the plasticity and other properties
of ice at or near its melting-point, on speculations on the same sub-
ject advanced by myself*, and, especially, to offer an explanation of an
experiment made by Professor James D. Forbes, which to him and
others has seemed to mihtate against the theory proposed by me, but
which, in reahty, I believe to be in perfect accordance with that theory.
In the year 1850, Mr. Faraday f invited attention, in a scientific
point of view, to the fact that two pieces of moist ice, when placed in
contact, will unite together, even when the surrounding temperature
is such as to keep them in a thawing state. He attributed this pheno-
menon to a property which he supposed ice to possess, of tending to
solidify water in contact with it, and of tending more strongly to so-
lidify a film or a particle of water when the water has ice in contact
with it on both sides than when it has ice on only one side.
In January 1857, Dr. Tyndall, in a paper (by himself and Mr.
Huxley) read before the Royal Society and in a lecture delivered
at the Royal Institution, adopted this fact as the basis of a theory
by which he proposed to explain the viscosity or plasticity of ice,
or its capability of undergoing change of form, which was pre-
viously known to be the quality in glaciers in virtue of which their
motion down their valleys is produced by gravitation. Designating
Mr. Faraday's fact imder the term " regelation," Dr. Tyndall de-
scribed the capability of glacier ice to undergo changes of form, as
being not true viscosity, but as being the result of vast numbers of
successively occurring minute fractures, changes of position of the
fractured parts, and regelations of those parts in their new positions.
The iarms fracture and regelation then came to be the brief expres-
sion of his idea of the plasticity of ice. He appears to have been led
to deny the applicability of the term viscosity through the idea that
the motion occurs by starts due to the sudden fractures of j)arts in
themselves not viscous or plastic. The crackling, he pointed out
might, according to circumstances, be made up of separate starts
distinctly sensible to the ear and to the touch, or might be so slight
* Proceedings of Royal Society, May 1857. Also British Association Proceed-
ings, Dublin Meeting, 1857. Also Philosophical Magazine, S. 4. vol. xiv. p. 548.
t Lecture by Mr. Faraday at the Royal Institution, June 7, 1850 ; and Report
of that Lecture, Athenxuin, 1850, p. 040.
2D2
392 Boyd Society : —
and so rapidly repeated as to melt almost into a musical tone. lie
referred to sliglit irregular variations in the bending motion of the
line marked by a row of pins on a glacier by Prof. Forbes, as being
an indication of the absence of any cjuality that could properly be
called viscosity, and of the occurrence of successive fractures and
sudden motions in a material not truly viscous or plastic. I can only
\niderstand his statements on this subject by supposing that he con-
ceived the material between the cracks to be rigid, or permanent in
form, when existing under strains within the limit of its strength, or
when strained less than to the point of fracture.
** This theory appeared to me to be wrong*; and I then published,
in a paper communicated to the lloyal Society, a theory which had
occurred to me mainly in or about the year 1848, or perhaps 1850 ;
but which, up till the date of the paper referred to, had only been
described to a few friends verbally. That theory of mine may be
sketched in outline as follows : — If to a mass of ice at its melting-
point, pressures tending to change its form be applied, there will be
a continual succession of pressures applied to particular parts —
liquefaction occurring in those parts through the lowering of the
melting-point by pressure — evolution of the cold by which the so
melted portions had been held in the frozen state — dispersion of the
water so produced in such directions as will afford relief to the
pressure — and recongelation, by the cold previously evolved, of the
water on its being relieved from this pressure : and the cycle of
operations will then begin again ; for the parts re-congealed, after
having been melted, must in their turn, through the yielding of other
parts, receive pressures from the applied forces, thereby to be again
liquefied and to proceed through successive operations as before.
Professor Tyndall, in papers and lectures subsequent to the publi-
* While the offering of my own theory as a substitute for Professor Tyndall's
views seems the best argument I can adduce against them, still I would point to
one special objection to his theory. No matter how fragile, and no matter how much
fractured a material may be, yet if its separate fractured parts be not possessed of
some property of internal mobility, I cannot see how a succession of fractures is
to be perpetuated. A heap of sand or broken glass will either continue standing,
or will go down with sudden falls or slips, after which a position of repose will be
attained ; and I cannot see Itow the addition of a principle of reunion could tend
to reiterate the fractures after such position of repose has been attained. When
these ideas are considered in connexion with the fact that while ice is capable of
standing, without immediate fall, as the side of a precipitous crevasse, or of lying
without instantaneous slipping on a steeply sloping part of a valley, it can also
glide along, with its surface nearly level, or very slightly inclined, I think the
improbability of the motion arising from a succession of fractures of a substance
having its separate parts devoid of internal mobility will become very apparent.
If, on the other hand, any quality of internal mobihty be allowed in the fragments
between the cracks, a certain degree at least of plasticity or viscosity is assumed,
in order to explain the observed plasticity or viscosity. That fractures — both
large and exceedingly small — both large at rare intervals, and small, momentarily
repeated — do, under various circumstances, arise in the plastic yielding of masses
of ice, is, of course, an undoubted fact : but it is one which I regard not as the
cause, but as a consequence, of ilie plastic yielding of tiie mass in the manner
supposed in my own theory. It yields by its plasticity in some parts until other
parts are overstrained and snap asunder, or perhaps also sometimes shde suddenly
past one another.
Prof. J. Thomson on Theories and Experiments regarding Ice. 393
cation of this theory, appears to adopt it to some extent, and to endea-
vour to make its principles cooperate with the views he had previously
founded on Mr. Faraday's fact of so called " regelation "*.
Professor James D. Forbes adopts Person's view, that the dissolu-
tion of ice is a gradual, not a sudden process, and so far resembles
the tardy liquefaction of fatty bodies or of the metals, which in
melting pass through intermediate stages of softness or viscosity. He
thinks that ice must essentially be colder than water in contact with
it ; that between the ice and the water there is a film varying in
local temperature from side to side, which may be called plastic ice,
or viscid water ; and that through this film heat must be constantly
passing from the water to the ice, and the ice must be wasting away,
though the water be what is called ice-cold.
There is a manifest difficulty in conceiving the possibility of the
state of things here described : and I cannot help thinking that
Professor Forbes has been himself in some degree sensible of the
difficulty ; for in a note of later date by a few months than the paper
itself, he amends the expression of his idea by a statement to the
effect that if a small quantity of water be enclosed in a cavity in ice,
it will undergo a gradual " regelation ; " that is, that the ice will iu
this case be gradually increased instead of wasted. In reference to
the first case, I would ask, — ^Vhat becomes of the cold of the ice,
supposing there to be no communication with external objects by
which heat might be added to or taken from the water and ice
jointly considered ? Does it go into the water and produce viscidity
beyond the limit of the assumed thin film of viscid water at the sur-
face of the ice 1 Precisely a corresponding question may be put re-
latively to the second case — that of the large quantity of ice enclosing
a small quantity of water in which the reverse process is assumed to
occur. Next, let an intermediate case be considered — that of a me-
dium quantitv of water in contact with a medium quantity of ice, and
iu which no heat, nor cold, practically speaking, is communicated to
the water or the ice from surrounding objects. This, it is to be ob-
served, is no mere theoretical case, but a perfectly feasible one. The
result, evidently, if the previously described theories be correct, ought
to be that the mixture of ice and water ought to pass into the state
of uniform viscidity. Prof. Forbes's own words distinctly deny the
permanence of the water and ice in contact in their two separate
states, for he savs, " bodies of different temperatures cannot continue
so without interaction. The water must give oft' heat to the ice, but
it spends it in an insignificant thaw at the surface, which therefore
tvastes even though the water be what is called ice-cold." Now the
conclusion arrived at, namely, that a quantity of viscid water could be
* I suppose the term regelation has been given by Prof. Tyndall as denoting the
second, or mending stage in his theory of ''fracture and regelation." Congela-
tion would seem to me the more proper word to use after fracture, as regelation
implies previous melting. If uiy theory of melting by pressure and freezing again
on relief of pressure be admitted, then the term regelation will come to he quite
suitable for a part of the process of the union of the two pieces of ice, though not
for the whole, which then ought to be designated as the process of melting and
regelation.
S94 Royal Society : —
produced in the manner described, is, I am satisfied, quite contrary to
all experience. No person has ever, by any peculiar application of
heat to, or withdrawal of heat from, a quantity of water, rendered it
visibly and tangibly viscid. We even know that water may be cooled
much below the ordinary freezing-point and yet remain fluid.
Professor Forbes regards Mr. Faraday's fact of regelation as being
one which receives its proper explanation through his theory described
above ; and, in confirmation of the supposition that ice has a tendency
to solidify a film of water in contact with it, and in opposition to the
theory given by me, that the regelation is a consequence of the low-
ering of the melting-point in parts pressed together, he adduces an
experiment made by himself, which I admit presents a strong appear-
ance of proving the influence of the ice in solidifymg the water, to be
not essentially dependent on pressure. This experiment, however, I
propose to discuss and explain in the concluding part of the present
paper.
Professor Forbes accepts my theory of the plasticity of ice as being
so far correct that it points to some of the causes which may reason-
ably be considered, under peculiar circumstances, to impart to a
glacier a portion of its plasticity. In the rapid alternations of pres-
sure which take place in the moulding of ice under the Bramah's press,
it cannot, he thinks, be doubted that the opinions of myself and my
brother Professor Wm. Thomson are verified*.
Mr. Faraday, in his recently published * Researches in Chemistry
and Physics,' still adheres to his original mode of accounting for the
phenomenon he had observed, and for which he now adopts the name
"regelation;" or, at least, while alluding to the views of Prof.
Forbes as possibly being admissible as correct, and to the explanation
off'ered by myself as being probably true in principle, and possibly
having a correct bearing on the phenomena of regelation, he consi-
ders that the principle originally assumed by himself may after all be
the sole cause of the effect. The principle he has in view, he then
states as being, when more distinctly expressed, the following : — " In
all uniform bodies possessing cohesion, i. e. being either in the liquid
or the solid state, particles which are surrounded by other particles
having the like state with themselves tend to preserve that state, even
though subject to variations of temperature, either of elevation or de-
pression, which, if the particles were not so surrounded, would cause
them instantly to change their condition." Referring to water in
illustration, he says that it may be cooled many degrees below 32°
Fahr., and still retain its liquid state ; yet that if a piece of the same
chemical substance — ice — at a higher temperature be introduced, the
cold water freezes and becomes warm. He points out that it is cer-
tainly not the change of temperature which causes the freezing ; for
the ice introduced is warmer than the water ; and he says he assumes
that it is the difference in the condition of cohesion existing on the
different sides of the changing particles which sets them free and
* Forbes ' On the Recent Progress and Present Aspect of the Theory of Glaciers,'
p. 12 (being Introduction to a volume of Occasional Papers on the Theory of
Glaciers), February 1859.
Prof. J. Thomson on Theories and Experiments regarding Ice. 395
causes tlie change. ExempUfying, in another direction, the principle
he is propounding, he refers to the fact that water may be exalted to
the temperature of 270° Fahr., at the ordinary pressure of the atmo-
sphere, and yet remain water ; but that the introduction of the
smallest particle of air or steam will cause it to explode, and at the
same time to fall in temperature. He further alludes to numerous
other substances — such as acetic acid, sulphur, phosphorus, alcohol,
sulphuric acid, ether, and camphine — which manifest like phenomena
at their freezing- or boiling-points, to those referred to as occurring with
the substance of water, ice, and steam ; and he adverts to the ob-
served fact that the contact of extraneous substances with the parti-
cles of a fluid usually sets these particles free to change their state, in
consequence, he says, of the cohesion between them and the fluid
being imperfect ; and he instances that glass vdll permit water to
boil in contact with it at 212° Fahr., or by preparation can be made
so that water will remain in contact with it at 2/0° Fahr. without
going oif into steam ; also that glass can be prepared so that water
will remain in contact with it at 22° Fahr. without solidification, but
that an ordinary piece of glass will set the water ofi'at once to freeze.
He afterwards comes to a point in his reasoning which he admits
may be considered as an assumption. It is " that many particles in
a given state exert a greater sum of their peculiar cohesive force
upon a given particle of the like substance in another state than few
can do ; and that as a consequence a water particle with ice on one
side, and water on the other, is not so apt to become solid as with
ice on both sides ; also that a particle of ice at the surface of a mass
[of ice] in water is not so apt to remain ice as when, being within the
mass there is ice on all sides, temperature remaining the same."
This supposition evidently contains two very distinct hypotheses.
The former, which has to do with ice and water present together, I
certainly do regard as an assumption, unsupported by any of the
phenomena which Air. Faraday has adduced. The other, which has
to do with a particle of ice in the middle of continuous ice, and
which assumes that it will not so readily change to water, as another
particle of ice in contact with water, I think is to be accepted as pro-
bably true. I think the general bearing of all the phenomena he has
adduced is to show that the particles of a substance when existing all
in one state only, and in continuous contact with one another, or in
contact only under special circumstances with other substances, ex-
perience a difficulty of making a beginning of their change of state,
whether from liquid to solid, or from liquid to gaseous, or probably
also from solid to liquid : but I do not thuik anything has been ad-
duced showing a like difficulty as to their undergomg a change of
state, when the substance is present m the two states already, or
when a beginning of the change has already been made. I think
that when water and ice are present together, their freedom to
change their state on the shghtest addition or abstraction of heat, or
the slightest change of pressure, is perfect. I therefore cannot
admit the validity of ]Mr. Faraday's mode of accounting for the
phenomena of regelation.
396 Boyal Society :^
Thus the fact of regelation which Prof. Tyndall has taken as the
basis of his theory for explaining the plasticity of ice, does in my
opinion as much require explanation as docs the plasticity of ice which
it is applied to explain. The two observed phenomena, namely the
tendency of the separate pieces of ice to unite when in contact, and
the plasticity of ice, are indeed, as 1 believe, cognate results of a com-
mon cause. Thev do not explain one another. They both require
explanation ; and that explanation, I consider, is the same for both,
and is given by the theory I have myself offered.
I now proceed to discuss the experiment by Prof. Forbes, already
referred to as having been adduced in opposition to my theory. He
states that mere cort/oc^ without pressure is sufficient to produce the
union of two pieces of moist ice * ; and then states, as follows, his
experiment by which he supposes that this is proved : — "Two slabs
of ice, having their corresponding surfaces ground tolerably flat, were
suspended in an inhabited room upon a horizontal glass rod passing
through two holes in the plates of ice, so that the plane of the plates
was vertical. Contact of the even surfaces was obtained by means of
two very weak pieces of watch spring. In an hour and a half the
cohesion was so complete, that, when violently broken in pieces, many
portions of the plates (which had each a surface of twenty or more
square inches) continued united. In fact it appeared as complete as
in another experiment where similar surfaces were pressed together
by weights." He concludes that the effect of pressure in assisting
'regelation' is principally or solely due to the larger surfaces of con-
tact obtained by the moulding of the surfaces to one another.
I have myself repeated this experiment, and have found the re-
sults just described to be fully verified. It was not even necessary to
apply the weak pieces of Avatch-spring, as I found that the pieces of
ice, on being merely suspended on the glass rod in contact, would
unite themselves strongly in a few hours. Now this fact I explain by
the capillary forces of the film of interposed water as follows : — First,
the film of water between the two slabs — being held up against gravity
by the capillary tension, or contractile force, of its free upper surface,
and being distended besides, against the atmospheric pressure, by the
same contractile force of its free surface round its whole perimeter,
except for a very small space at bottom, from which water trickles
away, or is on the point of trickling awaj' — exists under a pressure
which, though increasing from above do on wards, is everywhere, ex-
cept at that little space at bottom, less than the atmospheric pres-
sure. Hence the two slabs are urged towards one another by the ex-
cess of the external atmospheric pressure above the internal water
pressure, and are thus pressed against one another at their places of
contact by a force quite notable in its amount. If, for instance, be-
tween the two slabs there be a film of water of such size and form as
might be represented by a film one inch square, with its upper and
lower edges horizontal, and with water trickling from its lower edge,
it is easy to show that the slabs will be pressed together by a force
* " On some Properties of Ice near its Melting-Point," bv Prof. Forbes, Phil.
Mag. 1858, vol. xvi. p. 544.
Prof. Donkin on the Theory of the Attraction of Solids. 397
equal to the weight of half a cubic inch of water. But so small a film
as this would form itself even if the two surfaces of the ice were only
very imperfectly fitted to one another. If, again, by better fitting, a
film be produced of such size and form as may be represented by a
square film with its sides 4 inches each, the slabs will be urged toge-
ther by a force equal to the weight of half a cube of water, of which
the side is 4 inches; that is, the weight of 32 cubic inches of water or
1*15 pound, which is a very considerable force. Secondly, the film of
water existing, as it does, under less than atmospheric pressure, has
its freezing-point raised in virtue of the reduced pressure ; and it would
therefore freeze even at the temperature of the surrounding ice,
namely the freezing-point for atmospheric pressure. Much more
will it freeze in virtue of the cold given out in the melting by pressure
of the ice at the points of contact, where, from the first two causes
named above, the two slabs are urged against one another.
The freezing of ice to flannel or to a worsted glove on a warm
hand is, I consider, to be attributed partly to capillary attraction
acting in similar ways to those just described ; but in many of the ob-
served cases of this phenomenon there will also be direct pressures from
the hand, or from the weight of the ice, or from other like causes,
which will increase the rapidity of the moulding of the ice to the
fibres of the wool.
December 8. — Sir Benjamin C. Brodie, President, in the Chair.
The following communication was read : —
" On the Analytical Theory of the Attraction of Solids bounded
by Surfaces of a Class including the Ellipsoid." By W. F. Donkin,
Esq., M.A., F.R.S. &c.
The surface of which the equation is
i{x,y,z,h,k)=^0, (1)
is called for convenience " the surface {h, k)." The space, or solid,
included between the surfaces (//p A), {h.,, A), is called " the shell
f '\ /iji" and that included between the surfaces (h, A\), (h, Ac.^) is
called " the shell (h, /.* )•" [This notation is borrowed, with a slight
alteration, from Mr. Cayley.] It is assumed that the equation (1)
represents closed surfaces for all values of the parameters h, /r, within
certain limits, and that (within these limits) the surface (/i, A) is not
cut by cither of the surfaces (h + d/i, A), (h, Ji-^dk). It is also sup-
posed'that there exists a value /i^ of /<, for which the surface {h^, k)
extends to infinity in every direction. Lastly, it is supposed that if A
be considered a function of x, y, z, h, by virtue of (1), the two fol-
lowing partial differential equations are satisfied :
in which ^(Ji) is any function of h (not involving k), and n is any
398 Royal Society.
constant independent of h and k. The following propositions are
then demonstrated : —
The potential, on a given external point, of a homogeneous solid
bounded by the surface (/«, k), varies as the mass of the solid, if h
vary while k remains constant.
The potentials, on a given external point, of the homogeneous
shells ( Aj, jf\, ( 7*2, h ) ^^^ proportional to the massiss of the shells.
The homogeneous shell (h, ,^1 exercises no attraction on an in-
terior mass.
The external equipotential surfaces of the homogeneous infinite-
simal shell (h^, , J, are the surfaces {h, k), in which h is arbi-
trary and A- invariable*. . k4-dk\
The potential of the homogeneous infinitesimal shell ( ^u ?. )
upon an exterior point, is
and upon an interior point, is
4t 77 1 /z X /*^" dh
— dk^p(h,)/ -— .
n J h, H^{n)
(In these expressions \^(A) is e" *^ , and k at the lower limit
in the first, is the parameter of the surface (h, k) which passes through
the attracted point. The density of the shell is supposed to be unity.)
/ fc"\
The potential of the finite homogeneous shell I h^, , , J (density
= 1 ) upon an exterior point (J,, rj, ^), is
in this expression it has been assumed (for simplicity) that h^ i^ inde-
pendent of k. Also h", h' are the values of A corresponding to k", k',
when h and k vary subject to the relation f (£,»;, iif,/<, A) = 0; and k, in
the last integral, is the function of A, I, rj, 4" determined by this relation.
The diiferential equations (2) are satisfied in the case of the ellip-
soid. For if we put its equation in the form
*' a. y' J. ^'
+ rf-r + -^^=A.
a~ + h b^ + h c'^ + h
it is evident on inspection that
^A d'k d'k_^/ 1 , 1 I 1 \
dx^ dy~ dz^ \d'^ -\-h b'-\-h c^ + h/'
and /dkY , /dkY , /dky dk „
In this case we find \P(h) = ('(d^ + h)(b- + k)(c^ + hY^^, and the
above general expressions lead to the known results.
• It is known that the last two propositions imply the first two (see Mr.
Cayley's " Note on the Theory of Attraction," Quarterly Journal of Mathematics,
vol. ii. p. 338) ; though this is not the order of proof in the present paper.
Geological Society. 399
GEOLOGICAL SOCIETY.
[Continued from p. 320.]
February 15, 1860. — Sir C. Lyell, Vice-President, in the Chair.
The following communications were read : —
1. " On the Probable Glacial Origin of some Norwegian Lakes."
By T. Codrington, Esq., F.G.S.
The lakes to which attention was called by this paper are those
frequently found situated at a short distance from the head of the
several Qords on the western coast of Norway. The tjord and the
valley in which such a lake or " vand " lies are parts of one great
chasm, with perpendicular sides, often thousands of feet high. The
valley generally shows traces of the former existence of a glacier,
and is now traversed by a rapid river, which falls into a vand or lake
six or seven miles long, rarely a mile wide, and very deep. The
lake is separated from the fjord by a mass of rolled stones, shingle,
and coarse sand roughly stratified, and sometimes rising 120 feet
above the lake. Through this an outlet has been cut to the fjord,
a distance varying from about one to four miles. On the side
towards the lake this mound is terraced ; and at the upper end of
the lake similar terraces are sometimes seen. The author, with
some doubt, attributes the accumulation of this terraced barrier to
glacial action.
2. " On the Drift and Gravels of the North of Scotland." By
T. F. Jamieson, Esq. Communicated by Sir R. I. Murchison, F.G.S.
In a former communication the author gave an account of some
features of the Pleistocene deposits along the coast of Aberdeenshire,
showing that in certain localities remains of marine animals occur, of
a character similar to those met with in the later Tertiary beds of the
(^lyde district, and, like them, indicating the presence of a colder
sea. In the present paper the author treated of the Drift of the higher
grounds in the interior of the country, more especially as regards
that part of Scotland lying between the Moray Firth and the Firth
of Tay. The following phaenomena were more particularly de-
scribed : — 1. The upper gravels, their distribution and origin ; 2.
tlie marine drift of the higher grounds and of the highland glens ;
3. the striated and polished rock-surfaces beneath the Drift ; 4.
the high-lying boulders, and the dispersion of blocks from the Ben
Muic-Dhui Mountains. The probability of extensive glacier-action
before the formation of the Drift, the extinction of the laud-fauna
preceding the Drift, and the sequence of events during the Pleistocene
period were then dwelt upon ; and the author expressed his opinion
that the following course of events may be supposed to have occurred
in the Pleistocene history of Scotland. 1st. A period when the
country stood as high as, or probably higher than at present, with
an extensive development of glaciers and land-ice, which polished
and striated the subjacent rocks, transported many of the erratic
blocks, destroyed the pre-existing alluvium, and left much boulder-
earth in various places. 2ndly. To this succeeded a period of sub-
mergence, when the sea gradually advanced until almost the whole
400 Geological Society : —
country was covered. This was the time of the marine drift with
floating ice. The beds with arctic shells belonged to it, and some
of the brick-clays are probably but the fine mud of the deeper
parts of the same sea-bottom. 3rdly. The land emerged from the
water, during which emergence the preceding drift-beds suffered
much denudation, giving rise to the extensive superficial accumula-
tions of water-rolled gravel that now overspread much of the sur-
face. This movement continued until the land obtained a higher
position than it now has, and became connected with the continent
of Europe. Its various islands were probably also more or less in
conjunction. The present assemblage of animals and plants gra-
dually migrated hither from adjoining lands. Glaciers may have
still been formed in favourable places, but probably never regained
their former extension. 4thly. The land sank again until the sea
in most places reached a height of from 30 to 40 feet above the
present tide-mark. Patches of forest-ground were submerged along
the coast. The clays and beds of silt, forming the " carses " of the
Forth, Tay, and other rivers, were accumulated, as well as the post-
tertiary beds of the Clyde, &c., described by Air. James Smith, the
shells of which agree with those of our present seas. 5thly. An
elevation at length took place, by which the land attained its present
level. As Mr. Smith has shown, this probably occurred before the
Roman invasion : but that man had previously got into the country
appears from the fact that the elevated beds of silt near Glasgow,
contain overturned and swamped canoes with stone implements.
February 29, 1860. — L. Horner, Esq., President in the Chair.
The following communication was read : —
" On the Lower Lias of the South of England." By Dr. T.
Wright. F.G.S.
The author first stated that the uppermost beds of the Lower Lias
are those containing Hippopodium ponderosum, and that the lowest
beds are those with Ammonites Planorbis, overlying a series of strata
containing Estheria, &c., which he separates from the Lias, under
the name of the Avicula contorta beds. The last rest on the grey
and red marls of the Keuper.
Dr. Wright then proceeded with the description of the A. con-
torta beds, including the " Bone-bed," having first enumerated the
authors who have written on these and the equivalent strata (Kos-
sener Schichten, &c.) on the Continent. The sections at Garden
Cliff, near Westbury on the Severn, at Wainlode Cliff, at Aust Cliff',
at Penarth near Cardiff, at Uphill near Weston-super-Mare, at Cul-
verhole near Axmouth, at Wilmcote and Binton near Stratford-on-
Avon, were described in detail as illustrating this series ; and General
Portlock's section of these beds in the North of Ireland was also
alluded to. Pecten Valoniensis, Cardium Rh(Eticum, and Avicula con-
torta are the chief molluscan fossils of this zone.
The next group of strata are those with Ammonites Planorbis and
Am, Johnstoni. Some of the foregoing sections expose these beds,
such as those at Uphill and Wilmcote ; but they can be still better
studied at Street in Somersetshire, where they have yielded so
Dr. Wright on the Lower Lias of the South of England. 401
many fine Enaliosaurian fossils. These beds are also well exposed
at Brockeridge and Defford in the Vale of Gloucester, and at Bin-
ton in Warwickshire.
IsastrtBa Murchisonce occurs in this zone, and Ostrea liassica is
very characteristic of some of its lower beds. Ichthyosauri and Ple-
siosauri of several species are found in this series ; the latter chiefly
in the lower part. Of the two known specimens of PI. mega-
cephalns, one was found in these beds near Street, Somerset, and
the other at Wilmcote, Warwickshire,
The Ammonites Bucklandi characterizes the next higher group of
strata, which are also known as the Lima-beds. These are well
seen at Lyme Regis, at the Church Cliff and from the Broad Ledge
to the shore, and yield several species of Ichthyosaurus, also Am.
Cony bear i, A. rotiformis, A. angukitus, A. Greenoughii, and A. tor-
tilis.
The Am. Turneri beds are next, and can also be studied at Lyme
Regis ; they have yielded three species of Ichthyosaurus. Am. semi-
costatus and A. Bonnardi belong to this zone.
The Am. obiusus beds succeed, between the Broad Ledge at Lyme
and Cornstone Ledge near Charmouth; they apparently have no
saurian fossils. A. Brooki, A. stellaris, A.planicosta, and A. Dudres-
sieri accompany^, obtusus.
The next zone is that of the Am. oxynotus, with A. lifer and A,
lacunatus. The beds with Am. raricostatus comprise (in ascend-
ing order) the Ammonite-bed, the Hippopodium-bed, the coral-
band, and the Gryphaea-bed, This zone is well seen near Chelten-
ham, at Lyme, and at Robin's Hood Bay in Yorkshire. Am. ar-
matus, A. nodulosus, and A. Guibalianus belong to the A. raricos-
tatus beds.
Dr. Wright then pointed out that the Avicula contorta beds, like
the Kossen beds, contain a fauna special to themselves, and might as
well be classed with the Trias as with the Lias. They have a
wide range in the South of England, South Wales, the Midland
Counties, and the North of Ireland. After some remarks on the
more important features of the several Ammonite-zones of the Lower
Lias, the author concluded by remarking that, as Quenstedt and
Oppel had observed, the Middle Lias could be similarly subdivided
by means of the Ammonites peculiar to its several stages.
March 14, 1860. — L. Horner, Esq., President, in the Chair.
The following communications were read : —
1. "On the Occurrence of Lingula Credneriin the Coal-measures
of Durham." By J. W, Kirkby, Esq. Communicated by T. David-
son, Esq., E.G. 8.
As the Lingula Credneri of Geinitz, formerly known only in the
Permian rocks (Lower Permian of Germany ; Marlslate of Durham
and Northumberland), has of late been found by Mr. Kirkby in the
Coal-measures at the llyhope Winning, near Sunderland, he offers
this notice as of interest both as to the discovery of another species
common to the faunae of the Carboniferous and Permian eras, and as
illustrative of some of the physical conditions which obtained during
402 Geological Society.
the deposition of the Upper Coal-measures of the North of England,
the occasional occurrence of this Lingula proving that marine con-
ditions prevailed at intervals in the Durham area during the accu-
mulation of those deposits.
The species now known to be common to the Carboniferous and
Permian fauna; (besides L. Credneri) are Terebratula Sacculus, Mart.
(T. sufflata, Schl.), Spirifera Urii, Flem. (Martinia Clannyana,
King), Sjnriferina costata, Schl. {Sp. octoplicuta. Sow.), Camaro-
phoria Crumena, Mart. (Terebratula Schlotheimii, v. Buch), CamarO'
phoria globulina, Phil. {Terebratula rhomboidea, Phil.), — on the au-
thority of Mr. Davidson ; Cythere elongata, Miinst., C. inornata,
M'Coy, Bairdia gracilis, M'Coy, — on the authority of Mr. Rupert
Jones ; Gy r acanthus formosus, Ag., — according to Messrs. King and
Howse ; Pinites Brandlingi, Lindl., Trigonocarpon Noeggerathi,
Brong., Sigillaria reniformis, Brong., Calamites approximatus, Brong.,
and C. incequalis {}), Brong., — collected by Mr. Howse in the lowest
Permian sandstone. From the preceding list of Carboniferous spe-
cies found also in the Permian strata of Durham, we are able (says
the author) to see at a glance the specific relationship (so far as at
present known) which exists between the life-groups of the later
palaeozoic periods. The generic affinity of these groups has long
been noticed. This affinity and other apparent indications of a
•want of systematic difference originated the proposal that the Per-
mian should be included in the Carboniferous system ; and Mr.
Kirkby considers that the existence of the several recurrent Carboni-
ferous species in the Permian rocks strongly supports this view,
and that " Permian " should be retained only as a subordinate term.
2. " On the Rocks, Ores, and other Minerals on the property of
the Marquis of Breadalbane in the Highlands of Scotland." By C.
H. G. Thost, Esq. Communicated by Prof. J. Nicol, F.G.S.
After noticing generally the mica-schist of the district, with its
limestone or calcareous schist, and occasional roofing- slate, the au-
thor proceeded to describe first the porphyry-vein (half a mile wide),
containing silver-ore, copper-pyrites, grey copper-ore, iron-pyrites,
and molybdena, and crossing a vein of non-metalliferous greenstone,
at Tomnadashan, on Loch Tay opposite Ben Lawers. He then
pointed out the probable connexion of the existing great valleys
with lines of fracture due to igneous violence. The veins at Ard-
tallanaig, containing heavy spar, and ores of zinc, copper, and iron,
were next noticed. At Correbuich there are two sets of veins in
the calcareous schist ; those having a North and South direction
contain argentiferous galena and traces of gold. The most eastern
hills on Loch Tay, in the neighbourhood of Taymouth abound with
quartzose veins containing copper-pyrites, iron-pyrites, and galena.
The iron-ore of Glenqueich, and the serpentine and chromate of iron
at Corycharmaig, where graphite and rutile also occur, were next
noticed. At Lochearn Head there are galena-veins in calcareous
schist ; here, too, some auriferous arsenical pyrites has been found.
Lastly the author described in some detail the lead-bearing veins at
Glea Fallich and Tyndrum, which have been worked for many years.
[ 403 ]
LIII. Intelligence and Miscellaneous Articles.
NOTE ON THE SPECIFIC GRAVITY OF ELECTRO-DEPOSITED
AMORPHOUS ANTIMONY*. BY G. GORE^ ESQ.
nPHE following experiments are intended to illustrate the range of
*• variation of specific gravity to which amorphous antimony is liable.
Ten bars, each 1^ inch long, were simultaneously formed, with
their ends uppermost, in two rows of five each, upon the two oppo-
site surfaces of a vertical sheet of silver, in a solution composed of
teroxide of antimony and hydrochloric acid ; and after being removed
from the silver, washed and dried, their weights were taken and
their specific gravities determined.
No. "Weight. Sp. gr. at 60° F.
1. 278-15 grs 5-7421
2. 241-24 „ 5-7534
3. 273-30 „ 5-7536
4. 254-52 „ 5-7609
5. 246-185 „ 5-7647
6. 243-66 „ 5-7653
7. 231-94 „ 5-7725
8. 219-56 „ 5-8223
9. 227-42 „ 5-8327
10. 236-215 ,, 5-8330
In the bars there were no cavities to which the diflPerences of
specific gravity could be ascribed.
Birmingham, March 31, 1860.
ON THE PRODUCTION OF OZONE BY MEANS OP A PLATINUM WIRE
MADE INCANDESCENT BY AN ELECTRIC CURRENT. BY M. LE ROUX.
If a platinum wire, not too large, be made incandescent by an elec-
tric current in such a manner that the ascending flow of hot air which
has surrounded the wire comes in direct contact with the nostrils, an
odour of ozone is perceived. The experiment may be made in the
following manner : — A very fine platinum wire (yjjth to -}^ih. of a
millimetre) 20 centimetres long is taken ; it is formed in any
shape, and supported in an almost horizontal position in any suit-
able manner. A glass funnel of 2 or 3 litres is placed over this,
so that the air has sufl[icient access to the wire. As the neck of the
funnel is usually too narrow, it is cut so as to leave an aperture
2 or 3 centimetres in diameter, on which is adjusted a glass chim-
ney of a suitable length ; the object of which is to cool the gases
heated by the wire. The wire is then made incandescent by means
of twelve or fifteen Bunsen's cells. The gas issuing from the chim-
ney is found to have the odour of ozone ; iodized starch-papers are
altered in a few minutes when placed over the chimney. In this
case the air passing over the incandescent wire undergoes a peculiar
modification by which it acquires the properties of ozone ; but whe-
ther this is effected by the electricity acting as a source of heat, or by
its own proper action, must be reserved for further experiments. —
Comptes Rendus, April 2, 1860.
* Compare Phil. Mag. S. 4. vol. xvi. ->. 452.
404 Intelligence and Miscellaneous Articles.
OBSERVATION'S ON THE USE OF INSOLUBLE COMPOUNDS
IN VOLTAIC PILES. BY M. BECQUEREL.
In tlie decompositions announced in 1837, effected on insoluble
substances placed in contact "with the negative pole of a couple or
battery, I was able to reduce large quantities of different metallic
substances, more especially chloride and sulphide of silver, and sul-
phate and phosphate of lead. These effects are analogous to the
decomposition of fused chloride of silver, which takes place when
this substance is immersed in acidulated water in contact with a
plate of zinc.
Many years afterwards I recurred to the subject, and showed the
advantage to be derived from the use of insoluble substances in the
construction of voltaic couples. The couples might be composed of
an oxidizable metal (zinc or iron), a single liquid, generally saline
water, and a conductor of tin, surrounded by one of the substances
mentioned — such as silver, lead, or copper minerals, and in particular
sulphate of lead.
One of the most important applications of these effects was the
electro-chemical treatment of silver and lead ores*, using in this
case the remarkable action produced by an oxidizable metal ou
sulphate of lead in presence of saline water. Since this time I have
frequently used these sulphate of lead batteries in my electro-che-
mical researches. They were piles with one liquid ; the oxidizable
metal was zinc placed in a sailcloth hag, or in a permeable vessel filled
with saturated solution of salt. The second conductor consisted of
a bar of charcoal, or a plate of copper, lead, or tin, in contact with
brine saturated with sulphate of lead, or holding it in suspension.
The contents of the vessel in which this latter solution was placed
was often 3000 litres. Six such couples, united as a battery, gave
pretty strong sparks. The intensity of their action depends on the
depolarization of the negative plate by the sulphate of lead which
is reduced, and by which the disengagement of hydrogen is pre-
vented. Besides, the liquid contains sulphate of lead in solution as
well as diffused ; for it is soluble in about fifty parts of the saline
solution. The permeable diaphragm serves to prevent the closing
of the circuit and the destruction of the effect of the pile, by the
precipitation of lead on the zinc when solution of salt is employed.
It is to be observed that the electromotive force of the couple is
the difference of the effect produced by the liquid on the zinc and
on the reduced lead, and that hence it is sufHcient to have a rod or
plate of tinned iron or of lead, as negative conductor in contact with
the sulphate of lead. For some years, masses of sulphate of lead,
produced in the manufacture of sulphuric acid at Dieuze, and sold
at alow price, have thus been reduced to the metallic state. In the
fusipn of the lead it is necessary to take suitable precautions, as it
f^'equently contains a little sulphate. — Comptes Rendus, April 2, 1860.
* Comptes Rendus,' vol. ii. p. 23; and Becquerel's Traits d' Electricity,
vol. ii. p. 355 et seq.
THE
LONDON, EDINBURGH and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE,
[FOURTH SERIES.]
JUNE 1860.
LIV. Crystalline Form not necessarily an indication of definite
Chemical Composition ; or, on the possible Variation of Con'
stitution in a mineral Species independent of the Phanomena of
Isomorphism. By Josiah P. Cooke, Jun., A.A.S., Professor
of Chemistry and Mineralogy in Harvard College, United
States of America *.
IN a memoir prescntccl to the Araci'ican Academy of Arts and
Sciences in September 1855 1, I described two new com-
pounds of zinc and antimony, which I named stibiohizincijle and
stibiotrizincijle, on account of their analogy in composition to
the metallic radicals of organic chemistry. The symbols of these
compounds are Sb Zn^ and Sb Zn^; and they are distinguished
by the high perfection of their crystalline forms, the last being
still further characterized by a most remarkable j)roperty of de-
composing water quite rapidly at 100° C. I stated in the same
memoir that crystals of these two compounds could be obtained,
containing proportions of zinc and antimony differing very widely
from those required by the law of definite proportions; and I also
traced out the relation between the composition of the crystals,
and that of the menstruum in which they are formed. It is my
object in the present paper to consider the bearing of these facts,
already fully described, on the idea of mineral species, and to
offer a few suggestions which I hope may be of service in de-
termining the true chemical formuheof many minerals, and thus
in simplifying the science of mineralogy. But in order to render
myself intelligible, it will be necessary to recapitulate very briefly
the facts in question, referring to the original memoir for the full
details.
* Communicated by tlic Author.
t Trausiictions of tlie American Academy of Arts and Sciences, New
Series, vol. v. p. ,'537.
Phil. Mag. S . 4. Vol. 1 9. No. 1 29. June 1 8G0. 2 E
406 Prof. J. P. Cooke on the Variation of Constitution in a
The crystals both of Sb Zn^ and Sb Zir"^ can be obtained with
great readiness. It is only necessary to melt together the two
metals in the atomic proportions, and when the metals are fully
alloyed; to proceed exactly as in crystallizing sulphur. The melted
mass is allowed to cool until a crust forms on the surface, which
is then broken, and the liquid metal remaining in the interior
poured out. On subsequently breaking the crucible, the interior
is found lined with magnificent metallic crystals, which, when not
tarnished by oxidation, have a silver-white lustre. In the course
of my investigations on these compounds, crystallizations were
made, or attempted, of alloys differing in composition by one
half to five per cent., according to circumstances, from the
alloy containing 95 per cent, of zinc, to that containing 95
per cent, of antimony ; hut only two crystalline forms were ob-
served, that of Sb Zn^ and that of Sb Zn^. The crystals of the
two compounds both belong to the trimetric system ; but they
differ from each other, not only in their crystallographic elements,
but also in their whole "habitus." Stibiotrizincyle crystallizes
in long acicular prisms, which group themselves together into
larger prismatic aggregates ; while stibiobizincyle crystallizes in
broad plates, which twin together on an octahedral face, and
form a very characteristic cellular structure. This very striking
difference in the character of the crystals proved to be an im-
portant circumstance in the investigation, as it enabled me to
distinguish with certainty between the two compounds, even
when the faces of the crystals were so imperfect that a measure-
ment of angles was impossible.
The most remarkable result of the investigation, and the one
to which I wish to direct especial attention, is the fact that
each of the two crystalline forms was found to be constant
under very wide variations in the per-centage composition of the
crystals. As this is a point of great importance, it will be
necessary to enter more into detail, considering in the first
place the crystals of Sb Zn^. The crystals of this compound are
obtained in the greatest perfection from an alloy containing the
two metals in just the proportions represented by the formula,
namely, 42*8 parts of zinc, and 57*2 parts of antimony. They
are then comparatively large, generally aggregated, and, as the
three analyses cited in the accompanying Table indicate, they
have the same composition as the alloy.
Composition of the alloy by
synthesis.
Per cent. Pei- cent.
Composition of the
analysis.
Per cent. Per cent.
crystals by
Sum.
of Zn.
of Sb.
of Zn
of Sb.
42-80
57-20
4315
56-93
10008
}>
>}
43 06
56-50
99-56
»
t>
42-83
57-24
10007
mineral species independent of the Phenomena of Isomorphism. 407
On increasing gradually the amount of zinc in the alloy up
to 48"7, the crystals continued to have the composition of the
alloy ; and the only difference which could be observed in their
character was that they were smaller, and more frequently
isolated. Between these limits the whole mass of the alloy ex-
hibited a strong tendency to crystalhzation ; and by pouring it,
as it cooled, from one vessel to another, it could be crystallized
to the last drop. On increasing the amount of zinc in the alloy
to 50'7 per cent., the amount of zinc found in the crystals was
uniformly less than it was in the alloy ; but no closer relation
between the two could be detected, owing, undoubtedly, to the
unavoidable irregularity in the crystallization of the alloys which
contained more than 50 per cent, of zinc. This arose from a
peculiar pasty condition which the liquid mass assumed at the
point of crystallization. Definite crystals, however, were ob-
tained from an alloy of 60 per cent, zinc containing 55 per
cent. ; above this the crystals became less and less abundant,
and gradually faded out, although the alloy of 86 per cent, of
zinc exhibited a radiated crystalline texture ; and a trace of this
structure could still be discovered even in the alloy containing
only 4 per cent, of antimony. It was very interesting to trace
the gradual fading out of the crystalline structure, as the cha-
racter of the phsenomenon was entii'cly analogous to that which
may be noticed in many crystalline rocks.
Finding that the crystalline form of Sb Zn^ was constant under
so great an increase of the proportion of zinc in the crystals, it
might be supposed that, on returning to the alloy of 42'8 per
cent, of zinc and increasing the amount of antimony, we should
obtain crystals containing an excess of antimony ; but so far is
this I'rom being true, that the slightest excess of antimony en-
tirely changes the character of the crystallization. On crystal-
lizing an alloy containing 41 '8 per cent, of zinc, not a trace of
any prismatic crystals could be seen ; but in their place there
was found a confused mass of thin metallic scales, which, as will
soon be shown, are imperfect crystals of Sb Zn^. Thus it appears
that, although perfectly formed crystals of Sb Zn^ can be obtained
containing 55 per cent, of zinc (that is, 12 per cent, above the
typical proportions), they cannot be made to take up the slight-
est excess of antimony.
Let us pass now to the crystals of Sb Zn'^^. In order to obtain
crystals having the exact typical constitution, it was found ne-
cessary to crystallize an alloy containing not more than 31-5 per
cent, of zinc. At this puint large compound crystals are obtained
corresponding to the large crystals of Sb Zu'* ; and the same was
true of alloys down to 27 per cent, of zinc. Between these two
limits (namely, alloys of 31 "5 and 27 per cent, of zinc) the cry-
2 E2
408 Prof. J. P. Cooke on the Variation of Constitution in a
stals formed were found to have the theoretical composition of
Sb Zv?, indicating of course a tendency towards this point ; but
on increasing or diminishing the amount of zinc in the alloy
beyond these limits, the composition of the crystals immediately
began to vary in the same direction as that of the alloy. The
crystals of Sb Zn^ containing an excess of zinc are smaller and
more frequently isolated than those having the exact theoretical
composition. A similar fact, it will be remembered, is true of
the crystals of Sb Zn^.
At the alloy of 33 per cent, of zinc, the definite crystals of
Sb Zn- begin to disappear, and arc succeeded by thin metallic
scales, which are obviously imperfect crystals of the same form.
This w'as established, not only by the obvious law of continuity
noticed in the different specimens (the perfect crystals gradually
passing into the scales), but also by the peculiar mode of twin-
ing, which was the same witli the scales as with the large cry-
stals, forming the peculiar cellular structure already referred to.
Moreover, the angle between two scales thus united was found
to be equal to the basal angle of the perfect crystals, at least as
nearly as could be measured. These scales continue up to the
alloy of 41*8 per cent, of zinc, becoming, however, less abundant
and less distinct. Several specimens of them were analysed; but
no regularity could be detected in their composition, except that
they all contained a much larger amount of zinc than the alloys
in which they were formed.
Crystals of Sb Zn^ containing an excess of antimony w^ere readily
obtained from alloys containing less than 27 per cent, of zinc.
They became more and more imperfect as the excess of antimony
increased, and finally faded out altogether in the alloys below
20 per cent, of zinc. It is evident, therefore, that definite and
perfect crystals of Sb Zn^ can be obtained with a large excess
either of zinc or antimony above the theoretical composition. It
is also evident that, of the two compounds, Sb Zn^ is the most
stable, — first, because it is formed to the exclusion of Sb Zn^ in
all alloys containing less zinc than the amount corresponding to
the typical composition of the last compound ; and secondly,
because the crystals retain the typical composition under quite a
wide variation (viz. between 31*5 and 27 per cent.) in the com-
position of the alloy.
The facts above stated are fully illustrated by the following
Table, which gives the results of a large number of analyses of
crystals of both compounds formed in alloys containing different
proportions of the two metals : —
mineral species independent of the Phanomena of Isomorphism. 409
Analyses of the Crystals formed in the Alloys of Zinc and
Antimony.
Stibiotrizincylc.
c crystals
s.
Stibiobizincyle.
Composition of
the alloys by
synthesis.
Composition of th
by analys
Composition
of the alloys
by synthesis.
Composition of the crystals
by analysis.
Per
cent,
of Zn.
Per
cent.
ofSb.
Per
cent,
of Zn.
Per
cent,
of Sb.
Sum.
Per
cent,
of Zn.
Per
cent.
ofSb.
Per Per
cent. cent.
ofZn. ofSb.
1
Sum.
70-40
66-50
64-50
60-60
58-60
56-60
54-70
52-70
56-76
50-70
48-70
46-70
44-80
43-80
42-80
42-80
42-80
29-60
33-50
35-50
39-46
4140
43-40
45-30
47-30
49-30
49-30
51-30
53-30
55-20
56-20
57-20
57-20
57-20
64-15
6100
53-50
55-49
55-00
50-39
49-92
48-26
47-47
46-89
46-45
48-66
46-77
44 26
44-04
43-15
43-06
42-83
35-77
39-00
41-44
44-42
45-09
49-29
50-05
51-42
52-53
53 il
53-55
51-34
53-23
55-73
55-96
56-93
56-50
57-24
99-92
*10000
99-94
99-91
100-09
99-68
99-97
99-68
1 10000
tl 66-66
1100-00
1100-00
flOO 00
tl 00-00
tlOO-00
100-08
99-56
100-07
3300
33-00
32-50
32-50
31-50
29-50
29-50
27-50
26-50
26-00
25-50
25 00
24-50
23-50
22-50
21-50
20 12
67-00
67-00
67-50
67-50
68-50
70-50
70-50
72-50
73-50
74-00
74-50
75-00
75-50
76-50
77-50
78-50
79-88
35-37 64-57 9994
35-40 64-60+100-00
34-62 64-92 ! 99-54
34-61 65-39 flOOOO
33 95 ; 66 09 i 10004
33-62 ' 66-38 iflOO-OO
33-62 I 66-38 tlOOOO
33-85 65-81 9966
32-08 67-60 99-68
30-74 6906 99-80
30-43 69-51 99-94
29-88 70-20 10008
28-76 i 71-24 100 00
27-93 ' 71-85 99-78
26-62 73-27 99-89
24-83 74-74 9957
20-58 79-42 10000
1 1
' 1
* In this analysis the antimony only was determined,
t In this analysis the zinc only was determined.
The relation between the composition of the crystals Sb Zn^
and that of tlie alloy in which they are formed, is discussed at
length in the memoir already referred to. It is there shown to
be a very simple function of the mass of metal which is in excess
in the alloy, and of the force which determines the union of the
elements in definite proportions. The whole order of these
phajnoinena seem to the author to point to the existence of a
power in the mass of metal which is in excess in the alloy, to
disturb the action of the force, whatever it may be, which tends
to unite the elements in definite i)roportions. There is, in the
first place, a strong tendency in the elements to unite and form
crystals having the exact typical composition ; and secondly,
this tendency is only overcome by a certain excess of either
metal in the alloy. Then, again, the crystals of one compound
obviously interfere with those of the other. This certainly has
the appearance of one force interfering with the action of another,
— the force of mass (if I may so call it) perturbing the action of
the chemical force. JUit it is not my object at present to enter
into a discussion on the cause of this variation. Moreover, since
410 Prof. J. P. Cooke on the Variation of Constitution in a
such a discussion must be based on purely hypothetical grounds,
we could not expect to arrive at any definite conclusion. The
facts will be viewed difi'ercntly according to the theory which
may be adopted in regard to that long-controverted subject, the
essential constitution of matter. Leaving, however, all theore-
tical considerations aside, there are certain practical bearings of
the observed facts on the science of mineralogy which are of
immediate application.
Here are two beautifully crystallized products, as well crystal-
lized as any that occur in nature, and yet the different specimens
of the crystals differ from each other so widely in composition
that any single analysis might lead to an entirely erroneous con-
clusion in regard to the general formula of the substance. Were a
chemist to analyse accidentally solely the crystals obtained from
an alloy containing 58*0 per cent, of zinc, he would at once de-
termine that the formula of the compound was Sb Zn'* ; and by
a like accident he might be led to any other formula between
this and Sb Zn^ : in fact, by an analysis of a number of spe-
cimens of needle-shaped crystals obtained from alloys of copper
and tin, Riefifel was led to several just such improbable for-
mulae; and in my own investigations it was not until I had
analysed a whole series of crystals, that the real nature of the
phsenomena becaiue apparent, and the true constitution of the
compounds determined. If, then, such great variations in com-
position are compatible with a definite crystalline form in these
furnace products, may not similar variations occur in the cry-
stalline minerals formed in nature ?
It is not necessary to make an extended investigation in order
to answer this question ; for the materials at our hands are suf-
ficient to give us a satisfactory reply.
There is a compound of antimony and silver called Discrasite,
which occurs in many localities crystallized in trimetric prisms
homoeomorphous with Sb Zn^. The formula of the mineral is
therefore probably SbAg^, which would require 71'5 per cent,
of silver ; but the per cent, as given by analysis varies between
75'25 and 78 per cent., and one analysis gives the per cent, as
high as 85. Further analyses of this mineral are required in
order to determine its constitution, but there can be no doubt
that it varies in composition like Sb Zn^.
Silver-glance is another highly crystalline mineral. Theore-
tically it should contain 87*1 per cent, of silver and 12'9 per
cent, of sulphur ; but in a specimen analysed by Klaproth, the
proportions were 85 and 15.
Again, the analyses of pyrrhotine (magnetic pyrites) give
results varying between 38*78 per cent, sulphur, 60'52 per cent,
iron (variety from Bodenmais), and 43'63 sulphur, 56'37 iron
mineral species independent of the Pkanomena of Isomorphism. 411
(variety from Bareges). The constitution of the mineral is still
uncertain ; but its true formula is probably Fe S, which would
require 36"4 per cent, sulphur and 63*6 per cent. iron. Lastly,
the analyses of antimony-glance give results varying between
Antimony 74*06, ^ Antimony 73'5,
Sulphur 25-94, ^"^ Sulphur 26-5.
The true formula of this mineral is undoubtedly Sb S^, which
would require only 72'88 per cent, of antimony.
Similar examples might be very greatly multiplied. Those
just cited were selected at random from the first few pages of
Dana's ' System of Mineralogy/ They are all examples of binary
compounds which occur almost chemically pure in nature ; so
that the phrenomena in question are not complicated by those
of isomorphism.
When we pass to minerals of more complex constitution, the
same pha3nomena can be made evident, although not quite so
easily, on account of the introduction of the phsenomena of sub-
stitution by isomorphous elements. It will not, however, be
necessary for me to cite examples ; for it is a fact perfectly well
known to all mineralogists, that, after making allowances for the
substitution of isomorphous elements, the various analyses of
such minerals as mica, hornblende, garnet, and tourmaline differ
very greatly from each other, — a difference, moreover, which no
mere error of analysis will explain, and which must therefore be
referred to an actual variation in composition. In the silicates
this variation in composition is made evident by the variation of
what is termed the "oxygen ratios;" and it is well known to
mineralogists that in many species this variation is very large.
For example, in mica the following ratios between the oxygen in
the base and acid liavc been observed in merely the Muscovite
variety: — 13: 10, 13i : 16, and 14| : 16; and similarly wide
variations might be pointed out in other well-known species. It
is in consequence of such variations as these that the general
chemical formulae of some of the best-known mineral species,
such as mica and tourmaline, are still uncertain; and in other
cases, where the true formula is probably known, the constitution
of the mineral has been determined quite as much from other
considerations as from the chemical analyses.
Sufficient has been said, I think, to show that variations in
composition similar to those which I have observed in zinc and
antimony occur in many minerals ; and I trust that the results
of my investigation will serve to throw light on this whole class
of phsenomena, which have so greatly perplexed mineralogists,
and rendered all strictly chemical classifications of mineral spe-
cies so unsatisfactory. This investigation has shown that a defi-
412 Prof. J. P. Cooke on the Variation of Constitution in a
iiite crystalline form is compatible with quite a wide variation of
composition^ and has in this way ])ointed out an explanation of
the variation observed in the mineral kingdom. But more than
this, the investigation has also indicated a method by which,
amidst all this variation, the true constitution of the mineral can
be determined.
In the compounds of zinc and antimony, although the definite
crystalline form was compatible with a wide variation in the
proportions of the constituent elements, yet the point corre-
sponding to the typical composition was marked by several un-
mistakeable properties, which clearly enough indicated the true
formula of the compounds. These properties are discussed at
length in my original memoir, and need therefore only to be
alluded to in this connexion.
It has already been stated that the crystals, both of Sb Zn^
and Sb Zn^, having the theoretical composition are, as a rule,
larger and more generally aggregated than those containing an
excess of cither metal. Moreover, in Sb Zn^ the general character
of the crystals appears to be modified by the change of compo-
sition, although the crystallographic elements remain the same.
Thus in the crystals having the theoretical composition, the
octahedral planes are greatly developed, giving to the crystals
the general appearance of a truncated octahedron *. But as the
crystals take up an excess either of antimony or zinc, the basal
planes become more and more dominant, and the crystals are at
last reduced to thin plates. In fact, so marked are these changes,
that, after a little experience, a person could tell the approxi-
mate composition of the crystals from their general appearance.
Similar changes in the appearance of many minerals are familiar
to the mineralogist. They are seen in calcite, heavy spar, Angle-
site, and others, and may serve as guides in tracing variations of
composition.
Again, the specific gravity of the crystals, both of Sb Zn^ and
Sb Zn^, was taken with great care through the whole series, and
the results are tabulated below. The union of the two elements
is attended with an increase of volume, and this increase is at a
maximum at the points corresponding to the theoretical composi-
tion. These points would therefore be marked in a set of crystals
by being points of minimum specific gravity; and they could be
determined with great accuracy by means of this property, even
in a series of alloys of the two metals which had not been cry-
stallized. This fact is illustrated by the following Table, reprinted
from the original memoir.
* See figure accompanying my original memoir.
mineral species independent of the Phanomena of Isomorphism. 413
Specific Gravities of Crystals formed in the Alloys of Zinc and
Antimony.
Composition of the
Composition of the
1
alloys.
crys
tals.
jMean spec
of crystals
by experi-
1 grav. of
zinc and
Expansion
in crystal-
Per cent.
Per cent
Per cent.
Per cent.
ment.
antimony.
lizing.
of Zn.
ofSb.
of Zn.
of Sb.
10000
7-153
7153
0000
*9600
4-00
7-069
7-133
0-064
*86 20
13-80
6-898
7-082
0-184
*76-30
23-70
6-769
7-032
0-263
70-40
29-60
61-20
35-80
6-699
6-975
0276
66-50
33-50
6100
3900
6 628
6-959
0-331
64-50
35-50
5856
41-44
6-596
6-948
0-352
62-50
37-50
55-53
44-47
6-506
6-933
0-427
60-60
3940
5500
45-00
6-440
6-931
0-491
58-60
41-40
50-39
49-61
6-396
6-909
0-513
56-60
43-40
49-95
50-05
6-388
6-906
0-518
48-70
51-30
48-66
51-34
6-404
6900
0-496
46-70
53-30
46-77
53-23
6376
6-891
0-515
44-80
55-20
44-26
55-74
6 3U
6-879
0-538
t42-80
5720
43 09
5891
6327
6874
0-547
*40()0
60-00
6-386
6-860
0-474
*35-00
65 00
6-404
6-837
0-433
33-00
67-00
35-37
64-63
6-401
6-838
0-437
J2950
70-50
33 62
66-38
6-384
6830
0-446
t27-50
72-50
33-85
6615
6383
6831
0-448
2()-50
73-50
32-08
(}7'J-2
6-400
6-822
0422
2600
7400
31-07
68 93
6-418
6-818
0-400
25 50
74-50
30-43
69-57
6-428
6-816
0-388
24-50
75-50
28-76
7124
6-449
6-807
0-358
2250
77-50
26-62
73-38
6-453
6-798
0-345
21-50
78-50
24-83
75-17
6-467
6-790
0-323
*15 00
85-00
6-564
6744
0-180
*1000
90-00
6-603
6-721
0-118
*5 00
95 00
6-655
6698
0-043
10000
6-677
6-677
0-000
* Alloys not cryslallized,
+ Point of typical composition of SI) Zn-*.
X Point of typical composition of Sb Zn-.
The point of typical comjiosition in the case of the crystals of
Sb Zu'^ was still further marked in a most decided manner by a
very remarkable property. It has already been stated that this
compound has the power of decomposing water with rapidity at
100° C. ; but this is true only of those crystals which have ap-
proximately the theoretical composition. During the course of
my investigation I determined the quantity of hydrogen evolved
by alloys of different composition during a given time, taking
care, of course, that the circumstances should be the same in all
cases; and I found that with the alloy containing 13 percent, of
zinc, there is an immense maximum, eontined at most between 2
jjcr cent, on either side, the alloy of 43 per cent, yielding over
414 Prof. J. P. Cooke on the Variation of Constitution in a
nine times as much gas as an alloy of 50 per cent., although the
crystals of the last were fully as definite as those of the first*.
It is evident from the above facts, that the points corresponding
to the theoretical composition of the two compounds of zinc and
antimony, are aho points of maxima and minima of various pro-
perties. Now I have no doubt that the same truth will be found
to hold in the mineral kingdom. In a mineral like tourmaline
or mica, for example, the specimen having the exact theoretical
composition may probably be discovered by examining a lai-ge
number of specimens, and discussing their various physical pro-
perties. All the physical properties may be of value in this
connexion, such as lustre, hardness, specific gravity, specific
heat, &c. ; and no mechanical rules can be laid down. Much
must depend on the discretion of the observer ; and in any cases
such properties v.ill be selected as are best adapted to the cir-
cumstances of the case. In comparing different crystals of the
same mineral, it is obviously important to select such as have
been formed in a different matrix ; for it is only with such that
we should be led to expect great variations of composition. It
is also evident that the phenomena would be complicated when
there has been a substitution of isomorphous elements; and until
the effect of such substitution on the physical properties can be
traced, it will be necessary to select specimens of as uniform a
constitution as possible.
With one other consideration I will close this paper. The
principle which has been here discussed must modify materially
our notion of a mineral species. The idea of a mineral species
has hitherto involved chiefly two distinct characters : — first, a de-
finite crystalline form ; second, a constant general formula ; and
any important variation in either of these characters has been
regarded as equivalent to a change of species. Rutile and anatase
are regarded as different species, because their crystalline forms
are slightly different, although both minerals have identically
the same constitution; and again, magnetite and Franklinite,
which have the same form, are regarded as different species,
because they have a slightly different composition. It is true
that the actual composition of a mineral may vary very greatly
by the substitution of isomorphous elements, and yet, if the ge-
neral formula remains constant, the species may not be changed.
But the extent to which such substitution can be carried without
changing the species is not so well settled among mineralogists
as could be desired, and the same rule is not applied to all species.
The difference between the varieties of garnet, for example, is as
great as that between the species magnetite and Franklinite.
Leaving, however, this point undetermined, all mineralogists
* See Table in the memoir before cited.
mineral species independent of the PJimiomena of Isomorphism. 41 5
have agreed that any essential change in the general formula was
inconsistent with the idea of the same species. The result, how-
ever, of my investigation is to show that the general formula of
a mineral species may vary also, or, as I should rather say, the
genei'al formula is not necessarily the actual formula of each given
specimen, but only the tyjncal formula of the species towards
which the mineral tends, and which it would unquestionably
reach if it could be several times recrystallized.
According to this view, the general formula represents not the
actual constitution of the mineral, but only a certain typical com-
position, which perhaps is never realized with any actual spe-
cimen. The fact that the composition of a mineral species
may be modified by the substitution of isomoqihous elements,
was first established by Mitscherlich, and has long been an ad-
mitted principle in mineralogy. We must now, as I think, still
further expand our idea of a mineral species, and admit that its
composition may be modified by an actual variation in the pro-
portions of its constituents. Thus it is that in mineralogy, as
in other sciences, we are led to admit the truth of that maxim
which every advance in true knowledge seems to verify, " Natura
non facit saltus.^'
While the results of my investigations thus serve to render
the idea of a mineral species less definite than before, I cannot
but hope that they will tend ultimately to simplify the whole
subject of mineralogy ; for not only may we expect to reduce the
number of mineral species, but also, by simplifying the general
formulae of those which remain, to classify the whole with a
greater precision than is now possible. To do this, however,
implies a careful revision of the whole subject-matter of mine-
ralogy on the principles above given,^a labour of which few can
appreciate the extent, except those who are familiar with the
methods of physical research. The work cannot be done by any
one person; and it is the chief object of the present paper to call
the attention of mineralogists to the importance of the subject.
I have not thought it necessary to dwell in this paper on the
obvious distinction between the pha^nomena here in consideration,
and those of isomorphism. It was shown in my previous me-
moir, that the variation in the composition of the crystals of
Sb Zn^ and Sb Zn^ could not be explained by this principle ; and
the distinction between the two classes of phenomena has been
still further illustrated by a recent investigation on the crystals
formed in alloys of copper and zinc, made in my laboratory by
Mr. F. H. Storcr. These crystals, which are undoubtedly niLx-
tares of isomorphous elements, give no indications whatever of
points of typical composition, — thus illustrating not only the
characters of an isomorphous mixture, but also the distinction
416 Dr. Lamout on Phtenomena observed during
between such a mixture and a true chemical compound. Ad-
mitting, then^ the possibility of a variation of composition in a
mineral species^ independent of the phenomena of isomorphism,
it becomes of importance to distinguisli this new class of phseno-
meua by a separate term ; and I would propose for this purpose
the word AUomerism. By this w^ord I would designate a vai-iation
in the proportions of the constituents of a crystallized coinpoundivith-
out any essential change in the crystalline form. If, then, we also
use the word typical io indicate the condition oi defnite composi-
tion, we may speak of those specimens of a mineral species which
contain an excess of one or the other constituent, as allomeric
variations from the typical composition. The degree of allomerism
would then be measured by the excess of the allomeric con-
stituent above the typical composition. Thus the crystals of
Sb Zu'^ containing 42"3 per cent, of zinc would be said to have
the typical composition; while those containing 55 per cent, of
zinc would be distinguished as an allomeric variety, the degree
of allomerism in this instance amounting to 12 per cent., and
zinc being the allomeric constituent. In the case of the
mineral Discrasite, it is probable that no specimen having the
typical composition has yet been analysed. Those specimens
whose analyses are given in Dana's ' System of Mineralogy,' arc
all probably allomeric varieties of the mineral, silver being the
allomeric constituent, and the degree of allomerism varying
from 4 to 7 ])er cent. It is unnecessary, however, to multiply
examples, as the above are sufficient to illustrate the use of the
term.
LV, On Ph(snomena observed during Total Eclipses of the Sun.
By Dr. Lamont, Astronomer Royal at Munich^.
[With a Plate.]
IN my yearly report for 1854, I have endeavoured to give a
novel explanation, and one that differed from all the views
hitherto entertained, of the violet prominences that are noticed
in total solar eclipses. According to the explanation there set
forth only in general terms, the phfenomenou is produced by
little masses of clouds which become condensed in our atmo-
sphere in the cone of the moon's shadow, owing to the depres-
sion of the temperature which takes place there. From the cir-
cumstance of there occurring in 18G0 in S])ain a total eclipse of
the sun which may be observed under very favourable conditions,
and the opportunity there will then be afforded for arriving at data
for confirming or refuting my hypothesis, I am induced to return
* From Dr. Laraont's Yearly Report on the Bogcnhausen Observatory for
1858 (Munich, I85f'); translated and communicated hy W, G. Lettsom, Esq.
Total Eclipses of the Sun. 417
to the subject, and to discuss more fully the details contained
in recent reports upon this matter, without, however, touch-
ing upon the fundamental principles set forth at page 8 of my
Yearly Ileport for 1854, with which I assume the reader to be
familiar.
At the outset I must remark that when in a dark room an
opening in a window-shutter, a' b' (Plate I. fig. 1), is observed
from c through a film of vapour AB, the visibility of the vapour
depends on the brilliancy of the entering light*. If the bril-
hancy is very considerable, the light from a b falls on the whole
breadth of de, and is reflected to the eye from all points of the
vapour, thus rendering the entire film of vapour visible, though
with very unequal intensity. The intensity will diminish from
/to d and from rj to c, because the angle of incidence and re-
flexion is more and more inclined; the greatest intensity will be
manifested in the space fg, where the light passes from the
opening direct through to the eye. The more the brilliancy of
the light that enters at the opening in the shutter diminishes,
the more must the visibility of the vapour decrease, beginning
from d and e ; and a limit is soon reached where the h;ide portions
ff/ and de disappear altogether, the part f(/ alone remaining
visible. We see from this, that when a surface of light of very
low intensity is observed through a mass of vapour, only that
portion of the vapour can be perceived which is between the eye and
the luminous surface.
If the opening a b is so disposed that the light beginning at a
goes on decreasing towards b, then in like manner the visibility
of the vapour will diminish from / towards ^, and will only be
extended over a certain portion of the space /y.
To render what has been stated a])plicable to the phrenomenon
of total solar eclipses, it is requisite, iu the first place, to foru)
a precise notion with regard to vapour. On examining carefully
the formation of clouds, especially as they frequently present
themselves to us in summer, it will be remarked. tbat the vapours
which congregate together form no regular covering, but a ragged
interwoven mass (tig. 2), consisting of thicker parts, and ])arts
growing less dense till they vanish altogether. It will further
be noticed that very frequently the vapour disappears at one
side or at a corner — melts away as it were — and is deposited on
another side.
As far, moreover, as the light is concerned which serves for
rendering objects visible during total solar eclipses, it consists of
* If an uncoated looking-glass is besprinkled with alum-water ami tlien
allowed to dry, a line coating is formed thereon, on looking through wliich
the same appearances arc presented as tinongh a mass of vapour. This
arrangement is suitable to the experiment in question.
418 Dr. Lamont on Phenomena observed during
a bright ring encircling the edge of the moon, and which at the
edge itself is tolerably intense, but the intensity of which dis-
appears very rapidly outwards. It is moreover to be remarked
that the light may render the masses of vapour visible in different
manners. With a certain density of the vapour, and with a certain
intensity (always tolerably subdued) of the source of light, the
transmitted light appears coloured reddish ; with a greater den-
sity of the vapour, the light appears ivhite ; and when the vapour
has attained a cloud-like density, the light becomes entirely
stopped, the mass of vapour appearing black.
Let us now take into consideration, laying aside entirely at
first all that relates to motion, what phsenomena a mass of vapour
between the observer and the ring of light attending a total
solar eclipse will produce.
First, let a portion of the moon's edge be covered with a mass
of vapour (fig. 3), ab cd; in that case the portion situated within
the disc of the moon disappears for the observer, as does also
that portion extending out beyond the ring of light, and there
remains nothing but an elevation between a and b, the height of
which depends on the width of the luminous ring, while its
colour is dependent on the circumstances stated above.
Suppose we have (fig. 4) a mass of vapour, a b, a corner of
w^hich juts out beyond the edge of the moon, we shall then have
a mountain-shaped prominence produced, as the figure shows.
If we have (fig. 5) a mass of vapour, a, touching the edge of
the moon with one corner, there will be seen at the moon's edge
a pi'ojection with small isolated spots.
Let us now examine also the motion. The motion is here
threefold.
1. A motion of the earth on its axis, whereby the w^hole atmo-
sphere, and consequently the masses of vapour suspended therein,
are carried along over the moon's disc from west to east.
2. A movement of the clouds in the atmosphere, brought about
by currents of air, whose direction, speaking in a general way, is
not subject to any rule.
3. A motion due to the vapour becoming dissolved or de-
posited.
The first of these three motions is alone regular ; and its con-
sequence would be that the masses of vapour would apparently
become covered up by the western limb of the moon, and would,
on the contrary, make their appearance again on the eastern
limb.
AVith respect to the second motion, only thus much can be
said, — namely, that it follows the course of the current of the air.
When, therefore, the mass of vapour takes its origin in the lower
current of aii*, its motion coincides with the direction of the wind;
Total Eclipses of the Sun, 419
but wheu the vapour forms in the upper current, its motion will
probably be contrary to that of the lower one ; this latter point,
however, is very uncertain.
With regard to the third motion, nothing can be laid down
theoretically respecting it. In a general way the consequence
is that the apparent motion, considered as forming a part of the
three mentioned above, will, both in amount and also in direc-
tion, be accidental. Nor are we able to lay down anything
more definite relative to the changes of form originating in the
motion. If in a cloud of uniform density (tig, 3) the motion
takes place in the direction c d, the elevation on the moon's limb
will remain tolerably steady, with the exception of its extension,
which alters with the breadth of the cloud. A projecting point
(fig. 4) apparently disappears behind the moon's limb if the
motion is from a towards b; a projection becomes converted
into a mountain -crest when the mass of vapour approaches
towards the moon's centre.
Some kind of motion, however, is always to be looked for ; for
it would be a most improbable case that all the three motions
mentioned above should just counteract each other.
If we compare the theoretical views hitherto promulgated with
observation, it will be seen that, generally speaking, observers
have not directed their special attention to the circumstances
that were essential to arriving at a decision ; nevertheless many
particulars in confirmation of my explanation may be derived
from the great number of reports and sketches that we have
before us. The sketch by Fearnley of the solar eclipse of the
28th of July, 1851, as observed by him at Rixhoft, seems to me
to be especially characteristic. See fig. 6 for a copy thereof.
The form proper to clouds is here so distinctly pronounced,
and extends so far away from the moon's edge, that it seems to
me impossible to look for the origin of the phsenomenon any-
where but in our atmosphere.
I select the following circumstances from the very instructive
report of Schmid, who observed the same eclipse at llasten-
berg.
In the first seconds of the totality, he at once perceived in the
corona "several hriyhter places of vnperfectly dejined form, some-
thing like separate, ivhite, very nebuloust y-blurred little cluuds."
When the sun broke forth in the form of a fine crescent of light,
he examined carefully the remaining part of the moon's edge,
which disappeared altogether after 1 minute and 55 seconds,
after being 40 seconds previously partially interrupted, so that
there yet remained only separate portions of the arc which repre-
sented the curvature of the moon's edge.
Schmid did not remark any protuberances at all during the
420 On Phanomena observed duriiu/ Total Eclipses of the Sun.
first 7 to 10 seconds; it was not till after that interval that a
red protuberance declared itself of a sudden on the north-east,
precisely at the place where, before, a nebulous white spot had been
seen. This protuberance did not proceed from within outwards
from the moon's limb, but was formed suddenly, as if "the red
of the protuberance had had a whitish nebulous covering removed
from off it." It was distinctly remarked how the disc of the
moon advanced over this protuberance and completely covered it
over in a few seconds. A second protuberance became visible
shortly after the first one, but somewhat more to the north, and
it disappeared simultaneously with the first one. A third pro-
tuberance towards the south-east remained visible only during
two seconds. On the western limb there appeared gradually
three larger and one very small protuberance, which all increased
in size by degrees, and so changed their shape that there is
hardly any way of explaining it but on the assumption that a
ragged mass of vapour traversed the moon's disc in a westerly
direction. The wind on the surface of the earth had a general
westerly course, but varied both in its direction and force. ^Ve
must therefore assume that the masses of vapour were formed in
the upper regions of the air, and were borne onward in a direc-
tion opposed to that of the lower current.
In the report of Dr. Moesta, who observed the total solar
eclipse of November 30, 1853, to the south of Pisco in Peru,
it is especially worthy of remark that, fifteen minutes prior to the
sun being totally eclipsed, the yet existing crescent of the sun
became suddenly "invested with a dark rose-coloured nebular
substance." The intensity of this covering kept on increasing,
so that at last the edges of the sun and moon could only be in-
distinctly made out. After the commencement of the total
eclipse, there was seen on the western edge of the moon a rose-
coloured elevation which had a southerly motion, and which dis-
appeared in a minute and twenty seconds, its colour having first
passed to orange and then to yellow. In addition thereto there
were observed on the northerly edge two completely dark protu-
berances, which were without doubt masses of vapour of greater
density. The sketch made by Moesta is shown in fig. 7.
On the occasion of the total solar eclipse of September 7, 1858,
which was observed by a commission of astronomers at Paranagua
in Brazil, there were seen on the eastern edge of the moon two
white prominences with a black border, and one prominence
entirely white, which were apparently hidden by the moon as it
advanced : three prominences of a reddish colour made their ap-
pearance by degrees on the western edge, and they would seem
to have increased slowly in size. Here also, therefore, we should
have to assume a motion of the vapour from east to west.
On the Vertical Currents of the Atmosphere. 4.21
Among the meteorological notices, we find it stated that about
three-quarters of an hour after the total eclipse, clouds approached
the suu from the eastward, which harmonizes with svhat we have
assumed above ; it must not, however, be overlooked that in the
morning rain-clouds came up from the west ; so that here, again,
the direction of the current of the air remains undecided.
It would be easy to gather from the reports before us on the
total solar eclipses that have been observed, many more addi-
tional hints that coincide with and support my explanation of
the red prominences; but I confine myself to what has been
stated above, and this the more from my being of opinion that
decisive facts have first to be arrived at by future observations.
It will be especially advisable to follow up the masses of vapour
that condense in the cone of shadow, — and to do so not only at
the moon's edge, but likewise in the aureole as far outwards as
the light extends, determining at the same time their magnitude
and the dii'cction of their motion ; perhaps, indeed, it might be
practicable to gain some information upon this head immediately
previous to the disappearance of the sun, and immediately sub-
sequent to its reappearance. The visibility of the masses of
vapour depends mainly on their density ; and that they are not
unfrequently of considerable density is proved by the occurrence
of prominences that are black, or which at least are bounded by
a black border.
LVI. On the Vertical Currents of the Atmosphere. By Henry
Hennessy, F.R.S., M.R.I. A., Professor of Natural Philosophy
in the Catholic Universitij (f Ireland^.
1. TT has long been recognized that, although currents of wind
JL in a direction nearly parallel to the horizon are those wliieh
usually prevail, the atmosphere is frequently subjected to vertical
and oblique motions among its particles.
Under favourable conditions these motions may acquire such
a development as to force themselves iqjon the attt-ntion of
observers, and thus become objects for meteorological inquiry.
The interesting researches of -M. Fournet upon the vertical cur-
rents of mountains, appear to have arisen from the opportimities
enjoyed by that physicist of studying such phenomena among
the Alps. Among the deep ravines and valleys, as well as along
the elevated slopes and escarpments of the Alps, a regular
periodicity in the action of vertical winds has frequently been
observed during the course of twenty-four hours, which has led
to the conclusion that their development depends upon changes
* From the Atlantis, No. V. Connnnnicated by the Author.
Phil. May. S. 4. Vol. 19. No. 129. June 1860. 2 F
422 Prof. Hennessy on the Vertical Currents
of temperature resulting from the presence and absence of the
sun. As it is no^ well established that the distribution and
changes of temperature in these islands are dependent upon other
influential causes besides the direct action of the sun*, we can-
not, in general, expect to find in our climate a similar diurnal
periodicity so distinctly defined as that observed in the centre
and south of Europe. Here, as well as on the Continent, moun-
tains are favourable to the production of inequalities of tempe-
rature, moisture, and density among the aerial strata, which
thus become liable to a multitude of disturbances, and especially
to the action of vertical currents. It seems to follow, that in
mountainous countries vertical currents have well-marked rela-
tions with the changes of the weather.
If, as usually happens, lakes exist among the mountains, the
mysterious occurrence called the " bore " is also thus explained.
The circumstance that the suddenly-formed wave thus designated
always proceeds from a side of the lake bordered by steep moun-
tains, immediately suggests such an explanation. Although a
similar idea has occurred to other inquirers, I may be permitted
to refer to an instance where a demonstration was presented by
met of the efficiency of vertical currents in producing the " bore "
on the surface of one of our Irish lakes. The fact that such a
sudden wave usually preceded a change of the weather in the
district surrounding the lake, led me to think that the study of
the effective cause of the bore itself might become of importance
in meteorology. But to do this, we should possess means for
observing the actual direction and, if possible, the force of the
atmospheric currents.
2. Hitherto all instruments which had been employed for
observing the wind were devised exclusively with reference to its
horizontal direction and intensity, from the simple wind-vane to
the most finished anemometer J. I have attempted to modify the
ordinary vane so as to make it an indicator of the actual direc-
tion of the current, both in altitude and azimuth. Instead of the
fixed surface against which the wind impinges in ordinary vanes,
I had a disc suspended at the tail of the vane capable of rotating
on an axis perpendicular to the line of direction of the instru-
* See Phil. Mag. for October 1858 ; also a letter from the author to
Major-General Sabine, " On the Influence of the Gulf-stream on the Win-
ters of the British Islands," Proceedings of the Royal Society, vol. ix. p. 324.
t In a letter to the Rev. T. R. Robinson, D.D., of Armagh. See Pro-
ceedings of the Royal Irish Academy, vol. vi. p. 279.
X Some time after the anemoscope had been devised, my attention was
called by my friend the Rev. Dr. Robinson, to a passage among the notes
to Dr. Darwin's poem of the ' Botanic Garden,' wherein the writer indi-
cates such an instrument ; but he seems never to have realized this idea,
and the apparatus which he proposed was essentially different from mine.
of the Atmosphere. 423
ment. A pair of flanges were attached to this disc in such a
manner that, when the whole was at rest and the air free from
motion, the flanges would be horizontal. With perfectly hori-
zontal currents, the flanges would still continue in the same
position, although the head of the vane would as usual move
about in azimuth. But if a current happened to be inclined to
the horizon, the flanges would be pressed upwards or downwards,
showing the direction and amount of the inclination, precisely as
the position of the head or tail of the ordinary vane shows the
direction and inclination of a current with reference to the meri-
dian. When we know the inclination of a given current to the
horizon, we can readily estimate its absolute force from its hori-
zontal force, as can be easily shown.
3. Let the origin of coordinates be at the centre of the axis
of the vertical disc ; ydx will represent an element of the area
of the flange. Let 6 represent the angle of inclination of the
flange, II the pressure exercised by the wind in a horizontal
direction upon a square unit of surface, and V the vertical pres-
sure exercised upon a similar unit. The entire moment of the
horizontal forces acting on the entire flange will be
H i sin Oxydoc,
and the moment of the vertical forces will be
V i cos dxydx.
Both of these moments tend to cause a rotation of the disc,
but in contrary directions : hence when the disc is in equilibrium
they must be equal, and therefore, because 6 is independent of
X and y, we shall have
IIsin6'=Vcos6>, V = Htan^; . . . . (1)
and if we write F for the absolute force of the wind, we shall
have
F = Hsec^ (2)
Hence it follows, that if we can observe the absolute direction of
the wind, we can estinuUe its vertical force as well as its absolute
intensity without any special instrument, using the results ob-
tained by the existing anemometers which give the horizontal
intensity.
4. A wind-vane or anemoscope, capable of showing the abso-
lute direction of an atmospherical current, having been con-
structed in accordance with my directions, I proceeded to make
some observations during the months of June, July, and August,
1857. It was ])laced on the top of a strong mast, about twenty-
six feet in height. The mast was fixed near the end of a large
garden, far from buildings. As my first series of observations
2F3
424 Prof. Hennessy on the Vertical Currents
were intended to be merely provisional, I did not make them at
specitic fixed hours, but at such times as presented disturbances in
the atmosphere, or which afforded sufficient leisure for continued
attention. A journal was kept, from which I make the following
extracts. Before doing so, it is proper to remark that by the term
" vertical currents " in these extracts, as well as in the title of this
paper, I do not mean currents actually perpendicular to the
horizon, but rather oblique currents with an upward or down-
ward tendency.
" June 28, 7 a.m. — Air perfectly still, flanges horizontal, head
of vane towards the east. 7.30 a.m. — Breeze with slight
vertical currents until after 8. The currents were upward from
the ground. The flanges were often perfectly horizontal, and
their mean angle of inclination was small. About 10 a.m., a few
fine scattered clouds (cirro-cumuli) were observed to move in a
direction contrary to the wind as observed near the earth.
"From 3 p.m. to 3.45. — Wind extremely gentle fromE.S.E.
Upward current, angle of inclination estimated at about 5°.
The upward currents often continued for several minutes to-
gether. The angle was sometimes almost imperceptible. The
sky became gradually overcast towards eveni)ig.
"June 30,10 a.m. — Sky completely overcast, strong wind from
E.S.E., rapid oscillations of the disc during the greater part of
the day. About 6 p.m., the wind blew in violent gusts from the
east, and the disc showed alternations of upward and downward
currents with occasional short intervals. These observations
led me to conclude that rapid currents of air cannot generally
advance with the same steadiness as currents of water; the greater
mobility and elasticity of the former fluid probably allow its
movements to easily acquire a species of undulation. Thus we may
account for the motions of the branches of trees, which generally
swing backwards and forwards, showing rapid variations in the in-
tensity of the wind. During breezes composed of a succession of
strong sudden gusts, it was difficult to estimate the inclination
of the flanges, as each fresh impulse drove the llange beyond the
angle due to the pressure, and before it had been sufficiently long
oscillating about its true position to allow a correct observation, a
fresh gust would perhaps drive it in a different direction,
" July 1, 9 A.:^r. — Wind X.E., strong breeze with vertical cur-
rents. The position of the flanges was sometimes steady for
many minutes, with a veiy small inclination; upward currents
appeared to predominate in duration.
" July 2, before 9 a.m. — Air still and warm, head of vane di-
rected to S.E. After 9 a gentle breeze from E. and E.S.E.,
with an upward tendency. The disc remained steady at a small
an sic, sometimes for two minutes together. Towards noon the
of the Atmosphere. 425
disc was more steadily upward^ while the breeze still continued.
The clouds were observed to move from W.X.AV. At 6.30 r.M.,
a gentle breeze from W.S.AV.; sky covered with light clouds;
steady upward tendency of the current ; very little waving of
trees. The Hanges sometimes retained the same inclination for
a quarter of an hour. 8.30 p.m., wind more brisk from
the west, but the disc still steady; sky beginning to become
overcast.
"July 3, 8 A.M.— Wind S.W. and S. ; air filled with heavy
clouds, floating at comparatively short distances from the earth.
Strong breeze with alternate up and down currents, the down-
ward currents lasting but for very short periods. 9.15 a.m.,
wind S.S.E. with light rain. Just before the rain the down-
ward currents became more prominent, the clouds moved from
S.W. 10.30 A.M., wind S.S.AV. with alternate upward and
downward currents.
" July 5. — Fine morning, clear sky, with a few scattered cu-
muli ; gentle breeze from S.W., alternating currents upward pre-
dominant. 2 P.M. — Cloudy sky, with the air almost still; slight
vertical currents. Rain from four to seven o'clock. 9 p.m. —
Wind N.N. "W., clearing the sky; temperature rapidly falling,
with downward currents. Towards midnight the sky was
almost perfectly clear, and the wind more westerly.
"July 6, 9 A.M. — Very strong breeze from N.W., with vertical
currents and rain. The alternations were sometimes rapid, and
the apparent angle of inclination very great; the disc rarely
continued steady in an inclined position, although it sometimes
remained for long intervals in a perfectly horizontal position,
with a strong wind. Rain a])pearcd to produce no remarkable
effect on the flanges, for it seemed to be shaken or blown off.
About 3 P.M., the wind was strong and steady from N.N.W.; the
movements of the flange were as follows during the course of a
few minutes : — Downward, 1 h minute ; upward, h min. ; level, ^
min. ; oscillating, f min.; down, r[ min.; up, 4 min.; oscillating,
\ min. ; level, h min. ; up, ^ min. ; oscillating, \ min. ; level, |
min. ; up, 1 min. ; down, ;[ min. The air was gradually filling
with broken masses of cumulo-stratus clouds. As they ai)peared
to approach the earth, downward oscillations of the fiange be-
came more manifest. Approaching four o'clock the wind blew
irregularly, with violent and sudden gusts of short duration. At
Ci P.M., a strong breeze, with currents having a downward ten-
dency ; towards seven the sky became a little more clear, and the
currents appeared to be alternately upward and downward, with
short intervals of 10 or 12 seconds. At 7.15 p.m. the wind
was from N.W., with alternate currents, the upward predomi-
nating, while the sky was becoming perceptibly more clear.
426 Prof. Hennessy on the Vertical Currents
The upward currents were decidedly longer in duration than
at 6 P.M.
"Qg^p.M. — Wind still from N.W. ; upward currents, with
alternating currents at intervals of about one minute.
" July 11. — Wind W. A beautiful day, with a few light clouds
scattered over the sky. During the afternoon, up to 5 p.m., a
strong breeze, with very decided upward currents. At short
intervals the disc oscillated, showing a downward tendency.
" July 14. — Before 9 a.m., the wind was E.S.E. ; a moderate
breeze with downward tendency. Light clouds were observed
to move in a direction opposed to the wind at the earth^s surface.
10.30 A.M., wind S.E. ; an increase of clouds (cumuli) ; both
vane and disc were oscillating ; downward tendency of currents
was marked. At 1 o'clock in the afternoon, a fog was seen out
at sea, which, as it approached the shore, ascended in clouds over
Howth.
" August 6, 10 A.M. — Wind N.E. ; alternate currents, down-
ward predominating. The sky was covered with light clouds,
and the temperature comparatively low.
" August 20. — An extremely fine and warm day, with a clear
sky. The air was nearly still; and the disc continued to indicate
faint and steady upward currents ; for the flange continued at an
upward inclination of a few degrees for long intervals, sometimes
exceeding one hour. The movements of smoke that could be
observed at the same time showed a similar tendency.
" August 21,7 A.M. — Wind E.S.E., with no vertical currents ;
after 8, the disc began to move, and the flange was some-
times inclined upwards at a very small angle. It frequently re-
mained perfectly level, although a very perceptible breeze was
blowing. After 10 a.m. the upward tendency became more
manifest, and it generally remained for long intervals inclined
at an angle of from about 5° to 8°.
" August 24, 5 p.m. — Before and during a heavy shower the
disc exhibited the presence of downward currents.
" September 3, 8 a.m. — Wind blowing in sudden gusts from
N,E. ; the disc showed vertical currents, chiefly with a downward
tendency; rain followed at about half-past nine."
5. The few results which were thus recorded seem to show that
the study of the non-horizontal motions of our atmosphci'c is
desirable, not only among mountainous districts, but that it may
form a portion of our general inquiries under all local circum-
stances whatever. It appears that the wind rarely blows parallel
to the surface of the earth, and that the air, while in rapid motion,
is always undergoing a process of undulation, whereby the direc-
tion of the axis of a current at any point above the earth is
changed alternately, so as to be more or less inclined upwards or
of the Atmosphere, 427
downwards, just as the direction of the wind in azimuth is fre-
quently observed to slightly oscillate about its mean position.
We may conclude, therefore, from sect. 3, that the absolute force
of the wind is always a little greater than its horizontal intensity,
as exhibited by the anemometers.
While such an undulatory motion of the atmospherical currents
may be generally due to the elasticity of the air and the mechani-
cal influence of terrestrial irregularities, many of my observations
were such as to clearly show the existence of true upward and
downward currents. In no other way can we account for the
steady inclination of the flanges of the anemoscope at times
when scarcely any horizontal wind was perceptible. When true
upward currents were prevalent, the temperature of the air
was usually increasing and the weather fine. Downward cur-
rents seemed to be usually preceded or accompanied by a sudden
decrease of temperature, and these currents themselves usually
preceded rain or unfavourable weather. Regular alternations of
both classes of currents were usual about noon or the forenoon
of clear days. The explanation of the last circumstance is ex-
tremely simple. It depends upon the manner in which the at-
mosphere acquires the greatest part of its heat during the day.
A small portion of the solar heat is immediately absorbed in
passing through the air, but the greater part reaches the ground,
whence it is imparted to the atmosphere immediately touching
it. The air so heated expands, and consequently, from its re-
duced density, it tends to penetrate upwards in currents through
the overlying strata, which at the same time fall downwards to
till up the vacancies. A species of convection, analogous to that
seen in a boiling or heated mass of liquid, is thus developed in
the air. The trembling of the air, often noticed over steam-
boilers, close to the chimneys of steam-vessels, and even on walls
and gravelled walks heated by the mid- day sun, is undoubtedly
due to the same minute and rapid currents which take part in
this process of aerial convection.
6. That there are more important vertical currents engaged
in ])romoting exchanges between the upper and lower strata of
tlic atmosphere, within a siiort distance from the earth, appears
manifest from experiments made by me in May 1858*. Ther-
mometers were sus})endcd at different heights, and under different
circumstances of exjjosure to the supposed currents. On days
when the sky was clear, and when, consequently, the direct in-
fluence of the sun in heating the ground was most decided, ob-
servations were made every minute, and sometimes every half
minute, during short intervals. More or less rapid oscillations
* Report of the British Association for 1858. Trausactioas of Sections,
p. 36.
428 Prof. Hennessy on the Vertical Currents
of the mercury were observed. In thermometers freely exposed to
the air, the mercury sometimes rose or fell three degrees Fahren-
heit in three minutes. The longest fluctuations did not occupy
more than six minutes. The fluctuations diminished the more
the thermometers were protected from the influence of the cur-
rents of air,
A further confirmation of these results is found in the Report
of the Director of the liadcliffe Observatory at Oxford, relative
to the meteorological observations during the year 1857.
The thermometrical curves exhibited a remarkable serration
during the day-time of the most brilliant months of the year.
This serration entirely ceased during the winter, and on gloomy
days at every season : its intensity seemed to increase with sun-
shine. It is readily explained by the action of small atmosphe-
rical currents alternately ascending and descending, the former
producing a sudden and brief elevation of the mei'cury, and the
latter a sudden and short depression. The curves referred to
were obtained at the Radclifife Observatory, by a very beautiful
a])plication of the waxed-paper photographic process; and the
results here noticed would probably never have been exhibited
by the ordinary observations at stated hours. I cannot refrain
from remarking that the success which has attended this portion
of the application of photographical registration to meteorology,
has much increased my confidence in its trustworthiness, while
it has inspired a feeling of deep regret at the loss which science
has sustained by the death of ]Mr. Johnson, to whose able
management and indefatigable labours these and many other
results are mainly due.
7. To such small currents we may attribute whirlwinds of
more or less magnitude, from those which we often observe on
dusty roads, to the grand and frequently dangerous phenomena
of the desert. ^Ir. Belt, who writes in the Philosophical !Maga-
zine for January ] 859, presents some very instructive observa-
tions on this subject. The ascending currents over dry ground
in the interior of Australia, were frequently observed by him to
carry leaves and dust to the upper regions of the atmosphere.
Often, when travelling over parched plains, this observer saw the
air quivering over the hot ground as if close to the wall of a fur-
nace ; suddenly a miniature storm arises, and after a few minutes'
violence it as suddenly ceases, while the quivering of the air is
no longer seen and the atmosphere does not feel oppressive. All
these phfenomena are obviously the results of more or less ener-
getic interchanges between masses of air possessing diff"erent
temperatures. The process of convection in this case is not of
a gentle and gradual nature, but takes place with fitful violence.
The phccnomcua here referred to seem to present on a small
of the Atmosphere. 429
scale the principal features of cyclonic storms and hurricanes.
These arc always preceded by inequalities of temperature in the
regions where they occur ; and it is extremely probable that such
inequalities take place in a vertical as well as in a horizontal
direction. The distribution of watery vapour must at the same
time be affected ; and this would again react upon the equilibrium
of the atmospherCj so as to favour the existence of ascending and
descending currents. The rapid oscillations of the barometric
column which usually precede hurricanes are thus doubtlessly
connected, not only with variations in the statical pressure, but
also with the irregular influence of vertical and oblique currents,
which at such times disturb the equilibrium of the atmospherical
column over the barometer.
8. The duration and energy of many of the vertical currents
which came under my observation, were such as to show that
currents of a greater order than those which take place by the
influence of the heated ground immediately beneath are some-
times developed among the overlying atmospheric masses. Such
currents being of much greater magnitude than those which would
account for the rapid fluctuations of the thermometer already
noticed, we may refer to them not only great interchanges of
temperature in different strata of the atmosphere, but also a very
efficient part in the production of ordinary winds. If an exten-
sive portion of the earth's surface becomes more heated than
other surrounding portions, the air will ascend and overflow
above the cooler air resting upon the unheated surfaces. The
cold air at bottom will at the same time tend to rush inwards, so
as to fill up the vacuum which the ascending currents would
have left above the surface of the heated ground. As the air
that overflows above does not rush into a vacuum, but penetrates
and mingles with masses of cooler air possessing nearly the same
density, its progress is considei-ably I'etarded, while at the same
time some of the vapour which it may contain is condensed so
as to assume a vesicular cloudy form. A corresponding retar-
dation in the motions of the air rushing in from tlie colder to the
warmer surface below, is also produced from the resistance of the
air lying over the hitter. The production of sea- and land-breezes
furnishes a complete and instructivt; illustration of these remarks.
INIany of the upward currents which I observed with the anemo-
scope during the summer mornings, were undoubtedly the pre-
cui'sors of the sea-breeze. Such currents continue to accomj)any
the production of the land- and sea-winds in a manner that I have
sometimes been able to observe by the suu)ke of steam-vessels
near the coast. Thus, on a warm day in June 1857, I observed
the simultaneous existence of the sea-breeze at Kingstown and a
slight motion of a few light clouds from the interior towards the
480 M. Poinsot on the Percussion of Bodies.
coast. A steam-ship far out at sea was proceeding towards
England, and the smoke was drawn by the gentle breeze into a
streamer extending for miles behind the boat. The streamer of
smoke appeared straight and perfectly horizontal over the surface
of the water, until it arrived at a point about a quarter of a mile
from the Hill of Howth, when it rose upwards with a gracefully-
curved outline, and it appeared to be gradually diffused in the
air situated vertically over the hill.
The influence of vertical and oblique currents in the atmo-
sphere is not only thus manifest in the comparatively limited and
local phenomena of sea- and land-breezes, mountain winds, and
whirlwinds, but it has also been appealed to in order to explain
the circulation of the great winds of the earth. Thus Maury, in
his attempt to exhibit the general laws of the great winds, pre-
sents a diagram in which ascending and descending currents are
distinctly indicated over different regions of the globe. Their
agency is also appealed to by other inquirers ; and their principal
seats of action seem to be indicated as the calm regions, that is
to say, the regions where horizontal winds blow with least in-
tensity. Observations with the aid of the anemoscope in the
regions of equatorial and tropical calms would therefore probably
serve to test the accuracy of the general views here alluded to.
The systematic study of the non-horizontal movements of the
atmosphere has scarcely been commenced ; but what little know-
ledge we possess of such movements shows that they are so closely
connected with some of the most important phsenomena of the
weather, that their further investigation is certain to be attended
with interestins: and valuable results.
LVII. On the Percussion of Bodies. By M. Poinsot*.
[Continued from vol. xviii. p. 259.]
Chapter V.
1. TN the very special cases hitherto treated f, we supposed
A that the motion of the body was due to the impulse of
a single force P having a certain direction, and we merely deter-
mined the percussion Q which the body was capable of producing
against a fixed point presented to it in a peculiar manner.
It now remains to treat the general question where the motion
of the body is due to the action of any given forces whatevei', and
where the percussion is required which this body can produce,
by any one of its points, against any fixed obstacle which it may
encounter.
* From Liouville's Journal, December 1859.
t See Phil. Mag. vols. xv. and xviii.
M. Poinsot on the Percussion of Bodies. 481
General Problem.
2. A free solid body being animated by given forces, any one of
its points C suddenly encounters a fixed point ichich compels the
body to change its motion; required the direction and magnitude
of the percussion which will he produced upon this obstacle.
3. The solution is not difficult to find ; for if we represent the
percussion on the fixed ])oint by Q, it is evident that a force — Q,
equal and contrary to Q, applied to the body at the moment of
the shock, would at that moment precisely destroy the velocity
of the point C.
In order to obtain the equations of the problem, therefore, it
will suffice to express the condition that, under the influence of
all the given forces, and of the unknown force — Q applied at the
point C, this point of the body acquires a velocity equal to zero ;
this sole condition being developed, will supply all that is neces-
sary for the determination of the magnitude and direction of the
required percussion Q.
Development of the Soltjtion.
4. Let us make the three principal axes of the body which
pass through its centre of gravity G our coordinate axes; and
represent by m the mass of the body; by ma?, m^, my- its
three principal moments of inertia; and by x, y, z the coordi-
nates of the point C.
The given forces may be reduced to three forces,
Y Y 7
-^0> ^ 0» ^0'
directed along the three axes, and to three couples
1*0^ ^^0' -'^0'
in planes perpendicular to these axes.
Similarly the unknown force — Q, applied at the point C, may
be decomposed into three forces,
X, Y, Z,
applied at the centre of gravity G and directed along the three
axes, and into three couples around these axes, whose moments
will be expressed by
Y^-Zy, Z^'-Xr, Xy-Y^-.
• 5. The system of all the forces is thus reduced to the three
forces
Xo + X, Yo + Y, Zo + Z,
applied at the centre of gravity along the axes, and to the three
couples
Lo + Zy-Yz, Mo + X^—Za', No + Ya?-Xy
in planes perpendicular to these axes.
432 M. Poinsot on the Percussion of Bodies.
6. Wc have now to find the velocity of the particular point C
under the influence of these forces and couples.
7. In the first place, the three forces applied to the centre of
gravity impart to every point of the body, and therefore to C,
the velocities Xp + X Yo + Y Z^+Z
■ } ) (■•■)
m m m ^ '
along the coordinate axes of x, y, z respectively.
8. In the second j^lace, the three couples tend to cause the
body to turn around these axes with angular velocities whose
respective values are
_Lo+Zy-Y^ _Mo + X^-Z^ __ No + Ya;-Xy
V — 2 J *? — Z)2 i ^ — 9 • V'^)
^ mcn^ mp^ nv^^
But it will easily be seen that, in virtue of these three rota-
tions, the point C will have, in the directions of the axes of
X, y, z, the velocities
qz—ry, rx—pz, 2)y-qx .... (3)
respectively. Consequently, by adding these velocities to the
three preceding ones, and representing by x, y, z the total velo-
cities of the point C along the coordinate axes of x, y, z, we shall
^ave . Xo + X
X— -^ + qz — ry,
m
■ Yq + Y ,
y= -^ +rx-pz,
■ Zq + Z ,
z=z-^-~-\-py-qx;
whence, by substituting the values of ^;, q, r as given in (2), we
deduce the three equations
r(Mo + X.g-Za7) _ ?/(No + Ya;-Xy) "1
x{^, + Yx-Xy) _ z{L,+ Zy-Yz) ^ [ ^ ^j^^
Zq + Z y{IjQ+Zy~Yz) ^^(Mq + X^ — Z^)
J
9. These are the equations which furnish at once the compo-
nents X, y, z of the velocity^ imparted to the point C of the body
by the given forces which animate the same, combined with the
unknown force —Q supposed to be applied at the point C itself.
10. But the force — Q being properly chosen, the velocity y
of the point C, and consequently each of the components x, ij, ~
of this velocity will beconu; zero.
Putting i; = 0, y = 0, 'z = 0, therefore, the formula3 (A) give
M. Poinsot on the Peraission of Bodies, 433
the following three equations : —
-«2^yX + (aV + 7V + aV')Y-7VZ=-«y Yo-a^:rNo+7^rLo, V . (4)
-alv^X-/3VY + («V + y^y2^aWZ=-«'/S'Zo-/3VLo +«^^Mo, J
from which the components X, Y", Z of the force — Q may be
found. By changing the signs of these components, we shall, of
course, obtain those of the required percussion Q.
Resolution of the preceding Equations.
11. The three equations (4) being of the first degree in
X, Y, Z, may at once be solved by known formulae. Thus if
X, Y, Z be represented by the three fractions
B' B' D'
we shall have for the common denominator the value
and for the numerators the values
~-T,= - [^-^(aV + zS-y + 7--^-) +7^(«V + /3y) +/3-^(«V + 7V) +«2.y3272]Xo
- jry (aV + ^Y + y^z^ + «-/9^) Yq -X!:{u^v'^ + /3V + 7^^^ + «V)Zo
+ .ryz(/3-^-7^)Lo-~(«V^ + 7¥ + 7'^H«V)Mo
'.V
, = -.ry (aV^ + /3V + 7' -' + «'/3-)Xo
-y.-(a2.r^ +/3y + 7'~- + /8V)Zo
+ c(7V + /3y + 7'~' + /3V)T^ + ^^■y~{7^'-«^)Mo
-a^(aV + /Sy + «'^^ + «'/3') No,
3
.^3^= -.ry(«V + ;Q^/ + 7'~-' + «V)Xo
-yz(«V -f- ^y + 7'-' + /3y ) Yo
+ a:(aV + ««y2 + 7-C-2 + a-7') ^io + '^7~(«' - ^') N 0-
12. If, then, in the expression
434 Prof. Clausius on the Dynamical Theory of Gases.
the preceding values of Nj, N^, N-, D be substituted, the required
percussion Q will be obtained as a function of the data of the
problem ; that is to say, of the three arms a, /3, 70/ inertia of
the body, of the given forces and couples Xq, Yq, Zq, Lq, Mq, Nq
which animate it, and of the three coordinates .r, y, z of the
point C of the body where the obstacle is presented.
13. The form of the above expressions shows that, in virtue
of the applied forces and couples, the actual percussion of the
body is composed of the percussions which would be produced
upon the same point if each of these given forces and couples
acted separately, and this should clearly be the case.
It may also be remarked, that all these general formulse may
be verified by applying them to the particular cases treated in
the first two chapters. By so doing the reader may convince
himself of the perfect accordance between our results.
In conclusion, it will be well to add a short remark AA-ith
respect to the precise nature of the obstacle considered in the
problem which has just been solved. It is simply k fixed point
which is supposed to be capable of suddenly and totally arresting
the point C of the body which strikes it ; that is to say, of re-
taining it for an instant in the same position in space, just as if
this point C of the body had, for an instant, fallen into the inte-
rior of a hollow and resisting sphere of infinitely small radius.
It must also be borne in mind that, after the shock, this obstacle
is supposed to disappear entirely; for after the shock the body
merely retains a rotation around a spontaneous axis passing
through C, and therefore becomes incapable of striking an ob-
stacle presented at this point.
By means of its new motion, however, the body is capable of
striking with any other point C ; and the new percussion may be
found from the same formulae on replacing the old forces by the
new ones : we are thus led naturally to the theory of the singular
motions known as ricochets.
LVIII. On the Dynamical Theory of Gases. ^
By Professor Clausius. ^<v*a.- ^ ^ ^
To the Editors of the Philosophical Magazine and Journal,
Gentlemen,
^r^HE January Number of your Journal contains a very valu-
-I- able paper by Professor Maxwell, entitled " Illustrations
of the Dynamical Theory of Gases,^^ in which occurs (see
Prop. X.) a result opposed to an assertion made by me in a pre-
viously published paper*. Having waited in vain for the pro-
* PhU. Mag. Februarj- 1859.
Prof. Clausius on the Dynamical Them'y of Gases. 435
mised continuation of Prof. Maxwell's paper, I beg now to forward
my reply.
In my paper I consider the following question : a molecule fx
of a gas moves with a certain velocity in a space which already
contains many other molecules }n, m^, ?7?2j • • • ? ^^^ in so doing
occasionally strikes against and rebounds from the latter;
required the number of collisions made by fx in the unit of time,
or what is equivalent, the magnitude of the mean length of path
between two consecutive points of collision. In my solution I
confined myself to the case where the molecule /Lt moves, and the
others m, m,, . . . remain at rest ; but at the same time I asserted
that in the case where the latter molecules also move icith the
same velocity as fi, the number of collisions increases in the ratio
of 1 : ^. I did not prove this assertion, because for the object I
then had in new it was not necessai-y to enter into such parti-
culars. Since Prof. ]Maxwell, however, in his treatment of the
same subject, arrives at the ratio 1 : ^2 instead of 1 : 4, I feel
myself called upon to prove the accuracy of my former statement.
Let us first assume that fi alone moves, whilst m, m^, m^ . . .
remain at rest ; and let v be the velocity of fi, N the number of
moldcules at rest in the unit of space, and s the magnitude to
which the distance between the centres of yu. and any other mo-
lecule must be reduced before a collision can occui-. The number
of collisions during the unit of time will then be
fTTS^N.
If we now assume that the molecules m, m^, m^. . . also move,
we must replace the actual velocity v by the relative velocities of
the molecule yu. with respect to the molecules m, m^, ;«o . . .; and
since these relative velocities differ fi'om each other, the arith-
metical mean of all their values must be taken. Representing
this mean by r, the number of collisions will be
and consequently the ratio of the number of collisions in the two
cases will be v : r.
Thus far Prof. Maxwell and I agree, so that it will not be
necessary to enter here into the demonstration of the above for-
mulae ; we difter only in the determination of the mean value r.
Let wbe the velocity of any molecule ;«, and d the angle between
the direction of its motion and that of the molecule /i; the rela-
tive velocity between fx and 7n will then be
v'w* + v* — 2uv cos ■&.
When the molecules m, m^, m^ ... all move with the same velo-
436 Prof. Clausius on the Dynamical Theory of Gases.
city, in other words, when u is constant, and ^ alone variable
from one molecule to another, the mean value can be easily cal-
culated. According to Prof. Maxwell, the value in question is
whence, when u = v, follows r=v\^2. This value is incorrect,
however, as will be seen from the following considerations.
Since all directions are equally probable for the molecules 7«,
nil, iiic^, . . . , the number of those whose lines of motion make
angles between-^ and ■& + r/-& with the line in which /i moves will
have to the whole nuniber of molecules the same ratio that a
spherical zone with the polar angle ■& and the breadth d^ has
to the whole surface of the sphere, in other words, the ratio
Stt sin ^ d^ : 47r.
The number of such molecules in the vmit of volume is con-
sequently
N . i sin ^ d^.
In order to obtain the required mean value ;■, the last expression
must be multiplied by the relative velocity which corresponds to
it, the product integrated between the limits o and tt, and the
integral divided by N. Hence
-if
Vu^ + v^—'iuv cos ^ . sin ^ <fd.
JO
This gives at once
1 .l^uU-v''-i2uv)^-{u^ + v''^2uvf'],
6uv
whence we may deduce
r = v + l~, when n
and
„2
1 ^ 1
>■ = ?< -f- ' — when II > V.
When n = v, both results coincide in value with
r — 4-
o >
and thus verify my assertion.
I remain, Gentlemen,
Yours respectfullv,
Zuiifh, April 25, \m). R; ClaUSIUS.
[ 437 ]
LIX. On the Law of the Wave-lengths corresponding to certain
points in the Solar Spectrum. Sy Muxgo Poxton, F.R.S.E*
THE first attempt to find a law regulating the wave-leugths
corresponding to definite points in the solar spectrum was
made by Sir Isaac Xewton^ who chose for investigation the
boundary lines of the seven colours, being the only determinate
points then known. He adopted as the basis of his law a series
deduced from certain divisions of the musical chord. The same
series, however, may be obtained in a more palpable manner
from the following geometrical construction.
Round the point 0 describe a circle, and inscribe the equila-
teral triaug-le F A D. Draw the diameter A E bisecting the tri-
angle, and perpendicular to this diameter draw another, X Y.
Draw 0 B bisecting the arc A Y. Make A C equal to the side
of a pentagon inscribed in the circle, and then divide the arc
A F into three equal j)ortions by the points G and Z.
Regarding the whole circle as divided into 3G0 degrees, add
to this amount successively the number of degrees in the arcs
AB, BC, CD, DE, EF, FG, and GA, these arcs measuring re-
spectively 1-5, 27, 48, 60, 60, 40, and 80 degrees, thus produ-
cing the series 360, 105, 433, 480, 540, 600, 6i0, 730. Then
divide this series by the last term, and we obtain the following :
Co, 0-5625, 0-6, 0-66', 0-75, 0-833', 0-88', and l,a series from
which the ratios may be deduced in reference to the longest
wave as 1.
But it is more convenient so to alter the series as to make
1 = the mean wave. For this purpose draw the diameter z -M,
* Communicated by the Autlior, havin
Association at Aberdeen, September 1859.
Phil, Mag. S. 4. Vol. 19. No. 129. June 1860
been read before the British
2G
438 Mr. M. Ponton on the Law of the Wave-lengths
and to 360° add 200, being the number of degrees in the are
A M, so making 560 ; then dividing, as before, by 720, there
results 0'77' as the fraction corresponding to the mean wave in
the foregoing series, which nmst accordingly be divided by this
fraction. The quotients, taken in their reverse order, stand
thus: 1-2857, M428, 1-0714, 0-9643, 0-8571, 0-7714, 0-7232,
0-6429, the mean wave being =1.
The relative wave-lengths, however, as determined by Newton,
are represented, not by these numbers themselves, but by the
cube roots of their squares. The series then becomes 1'1824,
1-0931, 1-0470, 0-9761, 0-9023, 08411, 0-8057, 0-7449, the
length of the mean wave being =1. The ascertained length of
this last in air is 0-00002247 decimal parts of an English inch ;
and the lengths of the others are found by multiplying by this
quantity the above numbers ; so producing the following series,
which represents, according to Newton^s estimate, the extreme
wave-lengths between which the different tints of the solar spec-
trum lie, in decimal parts of an English inch : —
P . 0-00002657
^^^ 000002456
Urange 0-00002353
0-00002193
0-00002028
0-00001890
0-00001812
0-00001674
This accordingly is the estimate given of these wave-lengths
in all the English works on physical optics.
The next step in this inquiry was made by Fraunhofer, when
he discovered the fixed lines of the solar specti-um, and deter-
mined the wave-lengths corresponding to the points occupied by
the seven principal lines, which he designated by the letters
B, C, D, E, F, G, H. His observations are understood to have
been made with most careful accuracy ; and he left on record
two sets of values of these wave-lengths, agreeing as respects B
and D, but differing slightly as respects the other five. These
two sets of values, stated in decimal parts of a French inch, the
standard employed by Fraunhofer, are as follow : —
I. B 000002541, C 000002425, D 000002175, E 0-00001943, F.0-0000l789,
II. B 000002541, C 000002422, D 000002175, E 000001945, F 000001 794,
-1-3 -2 -5
I. G 0-00001585, H 0-00001451
II. G 0-00001587, H 000001464
-2 -13
No attempt has yet been successfully made to reduce these
Yellow
Green
Blue
Indigo
Violet
corresponding to certain Points in the Solar Spectrum. 439
numbers to any determinate law. The only relation hitherto
recognized is one subsisting in the second set, in which it is
fovuid that, if the reciprocals of the numbers be compared; the
square of that of F is equal to half the sum of the squares of
those of 13 and H, or F^ = |(Bf. + II^), the con*esponding num-
bers being
Yl . . . . =3107100
i(B^ + H^) . =3107068
Difference . 0000032
In the first set this relation does not subsist with nearly the
same degree of accuracy.
There is, however, a relation of more importance which may
be established by a very slight alteration upon the values of B
and D. Although the observed values of these two agree in
both series, neither of them can be regarded as correct to within
a ten thousandth part of its magnitude. Now by altering each
to a smaller amount than this proportion, we may establish the
remarkable relation B^=D''. Thus the observed value of B^
(taking seven effective numbers) is 1594052
And that of D« is 1593953
Difference only . 0000099
Dividing this difference, we make each 1594025, which gives
B = 2540844 (log 40^9780), differing from the observed value
by only -OOOOloG, and D = 2175112 (log 3374816), differing
from the observed value by only '0000112. As these alterations
are so trilling, and this relation of B'^ = D^" is very convenient,
there need be no hesitation in adopting it, and regarding the
above as the settled values of B and D.
There is a similar close approximation by which the value of
the wave-length of E may be deduced from those of B and D.
ItisB7D = E'i. Thus—
The observed value of E in the first series is . 1943000
The corrected log B 4049780 x 7 = 2-8348460
Add corrected log D ... . -3374816
Divide by 11 3-1723276
Gives for log E 02883934= 1942645
Difference only .... -0000355
This difference being much within the limits of probable errors
of observation, the abo\'e may be regarded as a convenient i-cla-
tion by which to connect the value of the wave-length of E with
those of B and 1), and the true logarithm of E may accordingly
be assumed as 0*288393 1. The nearer approacii to this value
exhibited by the first observed series may be viewed as one ad-
2G2
4)40 Mr. M. Pontou ow the Law of the Wave-lengths
vantage possessed by it over the second, which makes the value
of E 1945.
Another advantage presented by the first series will be brought
to light by the following arrangement : — Let the whole of the
wave-lengths be formed into an equicentral series of fractions,
thus, jj, g, J, ^, ^, ^, |r, ^, YV '"^ ^^'""^ ^^''^ ^'^^^^' ''
vided by each less, regarding E as the centre of the system.
Arranging the quotients in the order of their magnitudes, call
B.C E B C E D.D
E
G
H
=P' E =
E
= T, -rl=V, ~=<P/^=X
G
F
E
and :p- = i/r : the following are the values of these quantities
according to the two sets of observations, adopting in both the
above adjusted values of B and D, and in the case of the first
series, the above adjusted value of E.
1st set.
2n(l set.
Differences.
o = 1-751099
1-735549
0-015550
TT = 1-529968
1-526150
0-003818
p = 1-338832
1-328562
0010270
a = 1-307930
1-306347
0001583
T = 1-248298
1-245244
0-003054
V = 1-225643
1-225583
0-000060
(f> = 1-215826
1-212437
0003389
X = 1-119665
1-118310
0-001355
^= 1-085883
1-084169
0-001714
In this series we have p= -, v= — , and y = -V-, so that only
'^ a T ^ ylr •'
six of the nine members are primary.
Now if in both series the differences between the terms o, tt,
a, and i/r be taken, they will stand thus : —
Nos.
DIff.
Nos.
Diff.
0=1-751099
0-221131
2ncl Ser. o =1-735549
0-209399
77=1-529968
0-222038
TT =1-52(5150
0-219803
0- = 1-307930
0-222047
0- =1-306347
0-222178
1/^=1-085883
1/^ = 1-084169
1st Ser.
The near approach to a common difference of 0-222' is here
too striking to be overlooked, and too important to be thrown
aside, — the more especially as, in the case of the first series, the
alterations required to make tliis progression perfect arc very
slight — a second advantage which it enjoys over its rival. Further,
if in each case we take the sum of the first and middle terms, or
o + T, they will stand as under: —
corresponding to certain Points in the Solar Spectrum. 441
1st Ser. 0=1751099
r=l-248298
2-999397
2nd Ser.
0=1735549
T= 1-245244
2-980793
Thus in both cases the sum is very nearly 3^ but considerably
nearer in the first than in the second; and as o + t = 3 is a very
convenient relation, this may be viewed as a third advantage
presented by the first series, which requires only a trifling altera-
tion to make it fulfil this condition, as well as that of having
o, IT, a, yjr in arithmetical progression. These advantages
afforded by the first series overweigh the single advantage fur-
nished by the second, of presenting the before-mentioned rela-
tion of F'^ = |(Br + Hr), which is of little comparative value;
whereas the relations presented by the first series, when per-
fected, afford the great facility of rendering the whole of the
wave-lengths deducible from that of either B or D alone.
The first series, when properly adjusted to the several relations,
B5=D6,B7D = E'i,o = 7r-f0-222',7r=o--t-0-222',<7=f + 0-222',
and o + T = 3, will stand as under: —
Logs.
Nos.
Diiferences.
0 =0-2436268
1-752374
TT = 0-1847346
1-530152
0-222222'
p =0-1270422
1-339807
0-1903451
^0-222222'
o- =0-1165846
1-307930
0-031877
T =0-0960845
1-247626
0-060304"
V =0-0886501
1-226451
0021175
<f> = 0-0848012
1-215630
0-010821
>0-222222'
X = 0-0490882
1-119665
0095965
^=0-0357130
1-085708
0-033957_,
0-666666'
It will thus be perceived that, while the terms of the series are
nine in number, they arc divisible into three groups ; that the
sum of the first and middle term is 3; that each of the common
differences is ^ and their sum |, — relations sufficiently remark-
able in themselves, and easily borne in mind.
The following arc the values of the wave-lengths correspond-
ing to the fixed lines as deduced from the above series, and as
compared with the first set of observed values: —
Calculated.
Observed.
Differences.
B
2540844
2541000
-0000156
C
2423694
2425000
-0001306
D
2175112
2175000
+ 0000112
E
1942645
1913000
-0000355
F
1789289
1789000
+ 0000289
G
1583957
1585000
-0001043
H
1449944
1451000
-0001056
443 Mr. M. Ponton on the Law of the Wave-lengths
These differences are so far within the limits of probable errors
of observation, being all of them less than the least of the differ-
ences between tho corresponding members of the two observed
series, that there need be no hesitation in admitting them for
the sake of obtaining a series so regular as the foregoing, and
presenting the peculiar advantage of rendering the whole of the
wave-lengths deducible from that of either B or D.
In all calculations involving these wave-lengths, it will be
found more convenient to adopt, instead of the actual lengths
corresponding to any standard of mensuration, the relative wave-
lengths referred to that of B as unity, stating the others in frac-
tional parts; thus keeping the numbers independent of any
standard of linear measure. The wave-lengths and their loga-
rithms will then stand as under.
Relative wave-lengths referred to B as unity.
Logarithms.
Numbers.
c
T-9794999
0-9538934
D
1-9325036
0-8560588
E
1-8834154
0-7645667
F
1-8477034
0-7043103
G
1-7947653
0-6233979
H
1-7563733
0-5706545
Mean wave M
1-970] 116
0-9334940
It remains to compare the values of the wave-lengths corre-
sponding to the fixed lines, with those found by Newton^s series
for the boundary lines of the coloured spaces of the solar spec-
trum ; and for this purpose the latter must be reduced to the
standard of the French inch, when they will be found to stand
as under : —
Red. .
Orange
Yellow
Green .
Blue .
Indigo
Violet.
Newtou's wave-lengths.
(^0-000034939
1 0000033046
1 0-000033074
1 0-000030579
1 0-000019033
J 0-000017733
1 0-000016987
^0-000015705
Fixed lines mean ob.
B 0000035410
C 0-000034335
D 0-000031750
E 0-000019440
F 0000017915
G 0-000015860
H 0 000014575
corresponding to certain Points in the Solar Spectrum. 443
This Tabic shows that the Newtonian values are not recon-
cileable with those of Fraunhofer ; because they make the line B
lie beyond the red^ and the line H beyond the violet end of the
spectrum. The cause of this discrepancy is traceable to New-
ton's having made his observations on an impure spectrum;
Fraunhofer having been the first to obtain the pure spectrum,
produced by numerous fine equidistant lines, and from which
his wave-lengths were determined.
It is remarkable, however, that if we adopt Newton's primary
series without subjecting it, as he did, to the operation of taking
the cube roots of the squares, we shall obtain from it values for
the wave-lengths corresponding to the boundary lines of the seven
prismatic colours, agreeing much better with Fraunhofer's values
for the wave-lengths corresponding to the fixed lines.
This series, reduced to the standard of the French inch, stands
as under : —
Borders of colours.
Fixed Unes.
Red. . .
r 0-000027107
B
0-000025410
Orange .
Yellow .
Green .
] 0-000024094
C
0-000024235
} 0-000022588 Mean wave
1 0-000020330
D
E
0-000023719
0-000021750
0-000019440
Blue . .
] 0-000018070
F
0-000017915
Indigo .
1 0000016264
G
0-000015860
Violet. .
] 0-000015247
H
0-000014575
•■ 0000013554*
In this Table, not only are the fixed lines brought within
the spectrum, but each is referred to nearly its proper position.
It were desirable that fresh observations be made on the wave-
lengths corresponding to the border lines of the colours in the
pure spectrum, to ascertain whether these are accurately repre-
sented by the above series, or whether some other must be found
which shall more correctly exhibit their ruling law. The sub-
ject is worthy of the attention of the British Association, were it
only to prevent the existing error, in regard to the estimated
value of these wave-lengths, from being any longer perpetuated.
* This series makes the interval between the extreme violet and the ex-
treme red as 1 to 2, corresponding to the musical octave.
[ 444 ]
LX. On the Thickness of the Crust of the Earth. By the Rev.
Samuel Haughton, F.R.S., Fellow of Trinity College, and
Professor of Geology in the University of Dublin,
To the Editors of the Philosophical Magazine and Journal,
Gentlemen,
IN the April Number of the Philosophical Magazine, Arch-
deacon Pratt replies to my communication published in
December, 1859.
So far as the controversy is personal between us, it turns on
a very simple mathematical question, which I am quite willing
to leave for the decision of mathematicians. I regret that my
statements on this subject have not been sufficiently clear, though
I endeavoured to make them so, and must therefore beg the
favour of a few lines on the matter, before entering on the
other question raised by the present controvers)'.
I. The supposed "fallacy" in my reasoning.
For the convenience of reference, I shall call the two equations
in dispute (A) and (B). Archdeacon Pratt makes the following
statements : —
April, 1860.
" Professor Haughton .... re-
plies to my reasoning by showing
that he has differentiated equation
(A) right. This I never called in
question."
May, 1859.
" Equation (B) does not follow
from equation (A) hy differentiation.
In fact equation (13) assumes that
the law of density and ellipticity is
continuous throughout the whole
mass, solid and fluid, the solid
parts lying in strata of the form
and density they would have if they
were wholly fluid."
Archdeacon Pratt now admits that equation (B) may be ob-
tained from equation (A) by differentiation, but he has omitted
to see that I expressly state that equation (B) can only be ap-
plied to the fluid nucleus of the earth, and that I so apply it in
order to diminish by one, the total number of unknown quantities,
which must become known before the thickness of the earth's
crust can be determined. My words are, —
[Equation B] "^determines the relation which necessarily exists
between the law of density and ellipticity of the fluid portions
of the earth*.''
To prevent further misconception, I shall here briefly repro-
duce my argument, intended to show that our speculations on
the thickness of the earth's crust, if it have a crust at all, are
essentially hypothetical.
If the earth have a solid crust, containing a liquid nucleus
* Transactions of the Royal Irish Academy, vol. xxii. Science, p. 265.
On the Thickness of the Crust of the Earth. 445
inside it, its outer surface, as proved by observation, and its
inner surface, being the first fluid layer, ex necessitate rei, are
perpendicular to the force of gravity. The general condition
requisite for any surface of given specific gravity of the earth to
be perpendicular to gravity, is contained in equation (A), which
I here reproduce.
In this equation, the letters signify, —
e, the ellipticity of any layer ;
a, the equicapacious radius of that layer ;
p, the specific gravity of the layer ;
a, the equicapacious radius of the outer surface of the sup-
posed crust;
m, the ratio of centrifugal force to gravity at the equator.
This equation (A) applies to the outer surface of the crust,
and to the outer surface of the fluid nucleus, both of which are
perpendicular to gravity.
Let a, e denote the radius and ellipticity of the outer surface
of the crust ;
and let a„ ej denote the radius and ellipticity of the outer sur-
face of the supposed fluid nucleus : then equation (A), applied to
these two surfaces, will become
2p d.a'>e ., v 2 f' 2 /a ^
and
e
a
The first of these equations (A,) gives Clairaut^s theorem, but
teaches us absolutely nothiug of the structure of the interior of
the earth, except that it must be arranged in nearly spherical
strata, each of constant density, or in some way or other equiva-
lent to this.
The second equation (Ag) contains four definite integrals;
viz.
I. Cpa\
Jo
This integral extends through the whole earth, and is known,
because the mass of the earth is known.
i pa'^, and I
»/o Jo
II. \ pa^, and \ p-
da
These integrals extend through the fluid nucleus, and are uu-
446 The Rev. S. Haughton on the Thickness of
knowiij because they depend ou its masSj and moments of inertia.
If we assume the law of density, they will both become known,
or at least capable of evaluation, because the ellipticity is a
function of the density, by virtue of equation (B), which belongs
to the fluid nucleus, and to it only.
III. ry^
J a.
da
This integral extends through the crust, and is unknown. It
can only become known by our being acquainted with the law
of density, and also the Imo of ellipticity of the layers of the crust,
which are not connected with each other by an equation, as is
the case in the fluid portion of the earth.
If these preliminary difficulties were overcome, and the values
of the definite integrals known in terms of Rj and known
numbers, since e^ is also a function of aj (because it is included
in equation (B) as part of the fluid nucleus), the equation (Ag)
would become simply a function of aj and this unknown
quantity, the radius of the fluid nucleus, might be easily found.
The hypotheses requisite are the following : —
1st. The law of density of the fluid portions of the earth.
2nd. The law of density of the solid portions.
3rd. The law of ellipticity of the solid portions.
Of these three essential laws, I maintain that we are in igno-
rance, and must be content to remain so; and I challenge
Archdeacon Pratt, or any other person possessed of -' positive"
knowledge of the interior of the earth, to state what these laws
are. I am, indeed, well aware that a chance guess of Laplace's as
to the first law, has been considered by some almost an established
law of nature, and I would therefore ofi'er a few observations
upon it, to show how improbable it is that it should be even
an approximation to the real law of density that prevailed in
the layers of earth when altogether fluid, or in the layers of it
that are still fluid, if there be any such.
Legendre first applied the following law of density to the
determination of the earth's figure,
A .
p = — sin na,
where — ^
p = density of any layer,
a = the equicapacious radius, and
A, n are constants to be determined.
Laplace knew well what the meaning of this law was ; for in
discussing it in the Eleventh Book of the Mecanique Celeste,
he says, " Je vais presentement considerer la figure de la terre,
en la supposant formee d'un seulfluide compressible" {Mec. Cel,
the Crust of the Earth. 447
torn. V. p. 48). IMr. Hopkins and Archdeacon Pratt have adopted
this law, although, as it appeal's to me, it is utterly inconsistent
with the little we do know of the interior of the globe.
It is in the highest degree probable that the specific gravities
of the successive layers of the globe depend almost altogether
on their chemical composition, which is very varied, and only in
a very slight degree on the pressure to which they are subject ;
and that, consequently, a theory like that of Laplace, which
supposes the chemical composition uniform, and the density to
depend on an assumed law of compressibility, must be rejected,
as a matter of course, by every mathematician who wishes to have
a positive basis of fact for his speculations. For this reason, I
believe the charge which Archdeacon Pratt has brought against
me, of having attempted " an algebraical, not a physical problem
of densities," might with more fairness be brought against his
own unauthorized assumption of Laplace^s law, which he con-
siders " in itself a very probable law."
From a consideration of the igneous rocks of various ages of
the crust of the earth, many geologists have come to the conclu-
sion that the two outer layers of that crust are composed of
siliceo-felspathic rocks and ferro-calcifcrous eruptive rocks,having
average specific gravities of 2*55 and 3'00. The difference in
specific gravity of these layers is evidently due to the presence
of iron in the latter, and has no relation whatever to the pressure
to which they have been subjected. Such facts as this are com-
pletely ignored by the merely mathematical assumption that the
whole earth is composed of a homogeneous mass of fiuid following
a supposed law of compressibility. I believe, therefore, that I
am entitled to deny, as a matter of fact, that we possess any
positive knowledge of the interior of the earth ; and I shall re-
tain my conviction that such knowledge is beyond our reach,
until it is acquired by some process more legitimate than un-
founded hypotheses, which are contradicted by the few facts that
actually do come under our observation.
Before leaving this subject, it is worth while observing that
Archdeacon Pratt^s logic is as peculiar as his mathematics ; for
while he supposes that he has disposed of my sceptical argument
by the detection of a supposed fallacy in my mathematics, he
omits to perceive that, if I were really guilty of the fallacy, it
would strengthen my argument against our positive knowledge
of the interior of the globe, as it is plain that if I am not en-
titled to use the equation (B) to establish a relation between the
ellipticity and density of the fluid portion of the globe, I must
make an additional hypothesis, and therefore be forced to
discuss equations involving four unknown quantities instead of
three.
448 071 the Thickness of the Crust of the Earth.
II. Archdeacon Pratt's demonstration that the crust of the earth
cannot be va-y thin.
Before discussing this question, I would premise that I am
not an advocate for the idea, hekl by many physical geologists,
that the earth has a crust, and that its crust is very thin. I
believe it to be as unphilosophical to maintain it to be thin, as
to hold it to be thick, and that no good reason can be given for
either opinion.
The following idea of the interior of the earth is one which I
entertain myself with, but which I have no right to force upon
another, viz. that the earth is composedof three layers — of granite,
basalt or diorite, and meteoric iron and nickel, with an immense
cavity in the centre caused by centrifugal force — and that it is
completely solid at present. This, however, is a speculation, as
unfounded as any of those I have attacked; and I must return
to the demonstration that the eartVs crust cannot be very thin.
This demonstration consists of three parts : —
1. If very thin, the mountains would fall through.
2. If very thin, the floor of the oceans would be forced up.
3. If very thin, a semi-diurnal fracture would be caused by
the tides of the fluid nucleus.
I have already shown that Archdeacon Pratt's mode of con-
sidering the first of these questions is mechanically erroneous, as
he supposes the mountain mass to be in a state of tension,
whereas it is in a state of compression, and supports itself on the
principle of the arch.
In the second case, although the floor of the ocean is in a state
of tension, if the voussoirs be supposed to coincide with the radii
of the earth, yet we know so little of the real direction of the
main joints, that it is unsafe to speculate about them, although
their fan-shaped arrangement under the mountain axes would
appear to indicate a provision to sustain the weight, or rather is
itself a consequence of the superincumbent weight.
I prefer, however, to deny the validity of Archdeacon Pratt's
proof on the following grounds. As we know nothing of the
interior of the earth, I am as well entitled as any other person
to make hypotheses, and I accordingly make the follovv'ing : —
1 . The mountain chains float, like icebergs, on the surface of
the fluid nucleus, having deep roots penetrating far down into
the denser fluid below.
2. The liquid displaced by the roots of the mountains, finds
lodgement in cavities scooped out under the floors of the deep
oceans, thus restoring the hydrostatical equilibrium of the crust,
which is thinnest under the oceans, and thickest under the
mountains.
On a new Theoretical Determination of the Velocity of Sound. 449
3. The effect of the tide caused by the sun and moon is ren-
dered insensible at the surface by the great viscosity of the
liquid at the bounding surface, which can only be called a fluid
by courtesy. This viscosity distributes and destroys the pressure.
Let the foregoing hypotheses be assumed, which are quite as
likely as any hitherto adduced, and it follows easily that the
earth's crust, if it have one at all, need not exceed ten miles in
thickness.
In conclusion, I would observe that in this controversy I have
a natural advantage of position, which I am not prepared to re-
linquish. I deny our knowledge of the interior of the globe;
on this subject I maintain that our ignorance is absolute and
necessary. If Archdeacon Pratt possesses peculiar soui-ces of in-
formation on this subject, let him give us the benefit of his
knowledge ; but he may rest assured that something more is
necessary than reiterated assertion, and that to accuse an oppo-
nent of a fallacy which has no existence but in his own miscon-
ception of a mathematical principle, neither convinces others, nor
advances his own cause.
I am, yours sincerely,
Trinity College, Dublin, Samuel HaugHTON.
May 8, 1860.
LXI. On a new Theoretical Determination of the Velocity of Sound.
By the Rev. Samuel Earnshaw, M.A., Sheffield.
To the Editors of the Philosophical Magazine and Journal.
Gentlemen,
I AM perfectly aware the problem of the propagation of sound
is considered to have been solved; but notwithstanding this
I venture to offer the following new solution to the notice of the
philosophic world ; because it not only leads to a numerical result
quite diffei-ent from any before obtained from theory, and agree-
ing better with experiment, but likewise furnishes some new
results of an unexpected character, and affords besides a glimpse
into a department of nature which has hitherto remained her-
metically sealed. Laplace's ingenious suggestion of a, change of
temperature due to a sound-wave, brought the result of theory so
very near to that of experiment, tliat it has been thought un-
reasonable to require a closer agreement. But it is confessed
that the experiment by which the effect of a change of tem-
perature is obtained is one that is remarkably difficult to manage,
— one also in which errors of observation are greatly magnified
in the result: this is shown to be so, from the great differences
between the results of different experimentalists ; and I think I
may say that the requisite value of the coefficient (commonly
450 The Rev, S. Earnshavv on a new Theoretical
deuoted by k) is much greater than Dalton^s experiments warrant,
and than what would have been conjectured apriori to be its value.
In looking also at the determinations of its value, and also of the
value of the velocity of sound, I am a little suspicious that modern
experimentalists have suffered themselves to be biassed by a de-
sire to make experiment and theory agree. At any rate, if we
compare experiments made since 1816, when Laplace announced
his theorem for the correction of Newton^s result, with those
previously made, it is impossible not to notice a very sudden and
startling change ; and in the same spirit the value of k has been
gradually growing in the hands of experimentalists till it is now
large enough really to justify the opinion which has been ex-
pressed, that to Laplace is due the honour of having completed
the solution, which was begun in England, of the problem of the
propagation of sound. And, to speak candidly, it must be con-
fessed that Laplace's sagacious suggestion undoubtedly has the
air of a vera causa, although it requii'es a larger development
of heat by the sound-wave than seems probable. But its great
defect, if I may be allowed to consider it defective, is that the
result it gives does not come up to experiment. The theoretical
velocity, after being amended by Laplace's suggestion, still falls
short of the experimental velocity by 24 feet, if we take this last
to be 1090 feet ; and by 76 feet, if we take the velocity of sound
to be 1143 feet as determined by Derham, Llamsteed, H alley,
and the Florentine Academicians. It should be remembered also
that theory might apriori be expected to give a result exceeding,
rather than falling short of, experiment ; for theory assumes the
elasticity and fluidity of the atmosphere to be perfect, and we
have reason to think both are really in a slight degree im-
perfect ; and this is not likely to accelerate, but rather to retard
(if it at all affect) the propagation of sound-waves. Upon the
whole, after considering the matter in as impartial a spirit as
possible, candour obliges me to confess that Laplace's suggestion
does not furnish a sufficient cause. I do not deny that it may
be a cause; but it is not the whole. There is a cause, still
unrevealed, for the defect of the theoretical velocity. Euler
considered that some part of the error of theory might be due
to the incorrectness of analysis in assuming (-^1=1 previ-
ously to integrating the differential equation ; and certainly, as
this was an arbitrary step, it was reasonable to suppose it might
in some way have the effect of making the theoretical result
smaller than it would be were the equation integrated without
making use of approximative steps. When therefore I suc-
ceeded in integrating it without approximative steps, I was
disappointed to find that the theoretical velocity of a sound-
Determination of the Velocity of Sound.
451
wave remained the same as before. This caused me to examine
the question of the propagation of waves in an elastic medium
ab initio ; and the result is that I have, I believe, detected a
flaw in the problem as previously treated, which being remedied,
there results from theory a value of the velocity of sound which
agrees accurately with the experimental value found by Pictet,
and with the following remark of Young : — " From a com-
parison of the accurate experiments of Derham, made in the
daytime, with those of the French Academicians, made chiefly at
night, it appears that the true velocity of sound is about 1130
feet in a second;" and this agrees exactly with the value wdiich
I obtain by the theory, which I will now proceed to lay before
your readers.
1. There is a fundamental difference in the mechanical actions
of two elastic media, one of which is supposed to be continuous,
and the other to consist of particles separated by finite intenals.
Let A Z be an elastic medium ; divide it
by imaginary planes into extremely thin
slices D, E, F, . . . , so thin that each con-
tains only one layer of particles; in other
words, the thickness of the slices will be a..
equal to the distance between the particles
of the medium. Now according to the
common solution of the problem of sound,
the medium is supposed to be continuous ;
that is, any slice (as F) is pressed upon only by the two slices
(E, G) with which it is in immediate contact. And, correspond-
ing to this, any slice (F) is supposed to exert no direct pressure
on any slices beyond the two (E, G) with which it is in contact.
Hence all the motion which any one slice (F) has, it received
from one of its immediate neighbours (E), and transmits it
wholly to the other (G). This is the system of medial action
supposed in the investigation of the differential equation of sound
as commonly given.
But this supposes molecular action to extend from any one par-
ticle to those only which are nearest to it, — a supposition for which
there is no foundation whatever in nature. It is certain, how-
ever, that molecular action extends to a very small finite distance,
and therefore enables molecules which are separated by any
distance not exceeding that, to act on each other. Hence any
slice (F) is pressed upon by H, I, . . . as well as by G, on one
side ; and by 1), C, . . . as well as E, on the other ; and not a//,
but only some portion of, the motion which (F) receives does it
receive from E ; the rest comes from D, C, . . . ; and the motion
which F has received it does not wholly transmit to G, but it
distributes it among G, H, I, . , . the slices within reach of its
452 The Rev. S. Eamshaw on a new Theoretical
molecular action. This is the system of medial action supposed
in the investigation which I have to produce.
2. It is to be noticed, also, that when the medium is supposed
to be continuous, the ichole force exerted on F on one side is
supposed to be exerted by the slice E, and on the other by the
slice G; but on the other supposition, these forces are distri-
buted among the slices E, D, C . . . on one side, and G, H, I . . .
on the other, according to some rapidly decreasing law, which
we shall have to determine. Consequently the force which on
the first supposition is exerted by one slice (E) upon F, is on the
latter hypothesis exerted by E, D, C . . . unitedly ; so that the
force in the former case exerted by E alone is equal to the sum
of the forces exerted by E, D, C . . . in the second case.
3. Let z be the distance of any slice D from F, and let H be
at the same distance on the other side of F. Then we may repre-
sent by mf{z) the force exerted by either of the slices D, H on a
particle in F. Hitherto we have supposed the medium in equi-
librium, let it now be in a state of motion ; and for simplicity
let us suppose all the particles in any slice to be in the same state
of disturbance. Denote by x^, x, x' the disturbances of the slices
D, F, H at the time t. Then the whole force exerted by D and
H on a particle of the shce F
= mf{z -^x—x^— mf{z -\-3f^—x) = — mf {z) . {x,—2x + x-'],
neglecting powers of x—Xi and x^ — x above the first. Now
this step supposes that the rf//7//re displacements of any two par-
ticles which are within the sphere of each other's action, is so
small in comparison of their distance from each other, that the
square and higher powers of it may be neglected. The absolute
displacements may be of any magnitudes, subject to this con-
dition. Our results will therefore not be limited to small abso-
lute motions, but to small relative motions of particles within the
sphere of each other's action. Let now h be the thickness of
the slices ; and denote the disturbances of . . . D, E, F, G, H . . .
from their equilibrium positions by ....r,._2, ^r-u ^n ^r+i, Xr+2...
respectively. Then the equation of motion of any particle of the
slice F will be
'D']x\=mf' [h) . {Xr^i—2xj. + Xr+i)
+ jrif'{2h) . {Xr-2 — ^Xr + ^r + 2)
+ mf'{3h) . (av_3-2a;, + a^,+3)
+
4. It is not very difficult to exhibit symbolically the general
integral of this equation ; but that is no part of my present
object, which is to find the velocity with which any disturbance
is propagated through the medium. I shall therefore, for the
Determination of the Velocity of Sound, 453
sake of simplicity, assume the distm'bance to be of the type which
satisfies the equation Xr-=^A.rCOi>,{kt), A^. being a function of r
but not of t. By substituting this in the preceding dififerential
equation, we obtain
--yt2A,=m/'(A).(A,_,-2A, + A,+ 0
+ m/'(2A).(A,_2-2A, + A,+2)
+ 7n/'(3A).(A,_3-2A,+A,+3)
+
This being a linear equation of partial differences, its solution
will be of the form
A,=C«2'- + C'«-2'-, (1)
the quantity a being such as to satisfy the equation
-k'^ = mf'[h) . (a-a-i)2 + m/'(2A) . {a^-ct-^)'^+ ... (2)
These results may be exhibited in a more simple form by
writing a — a-'=2 ^ — 1 siu^, which reduces them to
^k^ = mf{h),&in'e + mf{2h)sm^20 + mf{Zh).sin^3d + .. . (3)
and
A^=2Acos(2r^ + a); (4)
.'. Xr =2Acos (2r^+ fl) cos {kt)
=Xcos{kt — 2r6— a) + Acqs {kt + 2r9 + a).
This is the general result for the type of wave which we have
assumed; and it indicates that there may be two waves of that
type travelling in opposite directions. For our purpose it will
be sufficient to preserve one of them. Hence we have
av=Acos(A-^-2r^) (5)
From this equation it results that if X be the length of a wave,
and V the velocity of its transmission,
e=^, (0)
and
+ 3«./(3.).e'3^f)V...y (D
5. Now in the case of all sounds which are audible to human
ears, X is immensely larger than h; and consequently for all
audible sounds, —^ = 1, -—^=1, &c. ; and hence the velo-
city of transmission of sounds of every pitch, audible to our
organs of hearing, though not absulutely the same, is sensibly the
Phil Mag. S.^4. \ol\^. No. 129. June 18G0. 2 II
454 On a new Theoretical Determination of the Velocity of Sound.
same, and equal to
hs/m.{l\f'{h)+2^.f'{2h) + 3^.f'{Sh)+ ...}i
From this formula we learn that every slice produces a term in
the expression for the velocity, so that there are as many terms
in the expression for the velocity as there are slices within the
radius of the sphere of action of any one particle.
6. From arts. 2 and 3 it is evident that the whole force exerted
upon a particle of the slice F by all the shces on one side of F
is mf{h) + 7nf{2h) + inf(Zh) + . . . ; and this is therefore the force
which we must suppose concentrated in the slice E, and an equal
force in the slice G, on the hypothesis of continuity. Hence if
mF {h) = mf{h) + mf{2h) + m/(3A) +...,
then
mViJi) =mf'{h) + mf'{2h) + mf'{dh) +,..;
and the equation of motion will be, for the case of continuity,
D<AV = »iF'(^) . {Xr-i — 2Xr + Xr+\).
From this we obtain, as before, the expression for the velocity of
transmission,
vel. =:h Vm . F'(A).
But in this case we know the velocity of transmission is ^/ ^,
the velocity determined by Newton,
.-. \/'ii=hVm.¥{h)
= h Vm . {f'{h) +f'{2h) +f{U) +...}K
7. Eliminating Vm between this equation and that of art. 5,
there results, finally,
_ - y\\f\h)+2\f\2h)+^'^.f{M) + . . . 1^
v-Vf..^- ^,(^^^ ^,^2^^_^ /'(3l)+.../-
Now the numerator of this fraction is of necessity larger than
the denominator ; and therefore, on the very face of it, this ex-
pression indicates that the actual velocity of sound is greater
than was found by Newton. It remains to determine the value
of this expression.
8. We assume that f{z), and therefore also f'{z), is some
simple inverse power of z. That power in the case o{f'{z) must
C
be greater than 3 ; for if /'(-) be equal to -g, then the expres-
sion in art. 5 gives the velocity of transmission
rc C C li
which is known to be infinite. The lowest possible value of the
M. G. Quincke on a new kind of Electric Current, 455
power is therefore 4. Assuming, therefore^ that /'(^) = -4-, we
find the velocity of the transmission of sound
-^22 + 3^
= v/
/^
l + 7Ti- + ^+^+--.
1 i- -1 i-
2'* "*" S'* "*" 4^ "^ ' * *.
_ v^Isg:
This put into numbers, taking >//* to be equal to 916 feet,
gives the velocity of sound equal to 1130 feet.
Thus we see that the error committed in calculating the velo-
city of sound, was not the leaving out the consideration of
the development of heat, but the supposing the medium of air
to be continuous. I am surprised to find the resvilt so much
aff"ected by_^a circumstance which appears trifling, — and the more
so, as the radius of the sphere of sensible molecular action is
known to be, though finite, very small. The assumption of
continuity is therefore by no means so allowable as we should be
inclined a priori to suppose ; and its effect on the motion of an
elastic medium is very much greater than was to be expected.
Sheffield, May 9, 1860.
[To be continued.]
LXII. On a neiu kind of Electric Current. By G. Quincke*.
UNDER the above title, the fifth Number of Poggendorff's
Annalen for 1859 contains an article of considerable
length, the leading points in which are contained in the follow-
ing abstract.
A^'hen pure water flows through a porous body, an electrical cur-
rent is elicited, — a fact established by the following experiments.
A plate of burnt clay is luted with seahng-wax between two
miliims. diameter (fig. 1), whose ends are
Fiff. 1.
glass tubes of 25
worked down smooth. A
pair of platina wires are
melted into the side of the
two tubes, and plates of '
platina arc riveted on to
those wires, the wires themselves being connected with the ter-
minals of a sensitive multiplier furnished with astatic needles.
The tubes A and B are made smaller at the ends, for the conve-
nience of connecting them with other tubes. The apparatus is
now filled with distilled water, care being taken that no air
* Commimicated by "W. G. Lettsom, Esq.
2 II 2
456 M. G. Quincke on a new kind of Electric Current.
remains in the clay plate. If, then, either by suction at B or by
some pressure at A, the fluid is driven from A to B through the
clay plate, there is indicated, at the instant the How of the fluid
begins, a deflection of the needles, due to an electric current
passing from A towards B. The platina plate B, then, on which
the current strikes last, behaves like the platiua plate of a Grove's
element. As soon as the passing of the water ceases, the needle
returns to its place, a polarization-current, however, in a contrary
sense to the primaiy current and to the flow of the fluid, being
called forth.
On changing the direction of the flow of the water, as by
means of suction at A, the multiplier indicates an electrical cur-
rent passing in the fluid from B towards A.
As with this form of the apparatus the flow of the fluid strikes
the plates dissimilarly, thus causing a want of precise similarity
in their conditions, the modification of the apparatus shown in
fig. 2, by which the flow of the fluid is not directed against the
platina plates at all, was arranged for the subsequent experiments.
With this view the tubes A, B of fig. 1 were closed at the end,
and two narrower tubes, C, D of fig. 2, were adapted to the side
between the open end of p. ^
the tubes and the platina
plates. With this arrange-
ment the fluid against
the plates remained un-
changed, while the water
flowed through C, the diaphragm, and D.
The pressure employed varied, according to the diaphragm
used, from a third of an atmosphere to three atmospheres.
Instead of the clay plate, other porous bodies were placed
between the tubes A and B of fig. 2 ; and the multiplier always
indicated a current coinciding with the flow of the fluid, and
which lasted as long as that flow did. On its ceasing, there was
a more or less strong polarization-ciu*rent in a contrary direction
to the primary one.
The substances thus examined were, —
Sdk,
Sulphur,
Linen,
Burnt clay.
Ivory,
Talc,
Glass,
Graphite,
Sand,
Bunsen's coal,
Fir-wood,
Iron,
Lime-wood,
Platina,
Oak,
which were applied in the following way.
M. G. Quincke on a new kind of Electric Current. 457
Some thirty layers of thin silk stuff were placed over each
other and attached over the tube A of the apparatus ; the tube
B was then adapted against the former, and the part separating
them covered thickly with sealing-wax. Owing to the wide
pores of the silk, considerably more water flowed through under
equal pressure than when the clay plate was employed. The
linen was used in the same manner.
The other substances were applied in the form of powder, in a
glass tube of the diameter of the tubes A and B of fig. 2. The
ends of these tubes, the length of which varied, according to the
substance employed, from 20 to 45 milliras,, were ground flat,
and over them were placed discs of the silk stuff spoken of, to
prevent the flow of the fluid carrying away particles of the sub-
stance under examination. In the case of Bunsen's coal the
tube was closed with plates thereof.
Platina was made use of in the spongy form, iron as filings.
The glass had been reduced to powder on an anvil. Ivory and
the various kinds of wood were employed in the form of sawdust.
It was endeavoured in vain to press water through a porous
plate of wood, for the plate had to be luted in dry; and on
becoming moist, even if cut perpendicular to the direction of the
fibres, it warped so much that it broke the sealing-wax or the
tube.
The direction of the electric current was not changed by add-
ing acids or solutions of salts to the distilled water, but it was
considerably weakened thereby.
For instance, on using a new clay plate 3'9 millims. thick,
and pressing distilled water through it, the needle of the multi-
plier was deflected up to the stop : on the addition of four drops
of pure hydrochloric acid to a pint and three-quarters of the
water, the deflection of the needle did not, under the same pres-
sure as before, exceed 15 or 20 degrees. A fm'ther addition of
twelve drops of acid weakened the electric current so much, that
a far greater pressure had to be applied to deflect the needle at
all. If the acid amounted to IG per cent, of the fluid employed,
no deflection whatever was observed, even under a pressure of
three atmospheres. On adding alcohol to the distilled water,
the deflection of the needle was increased.
The question arises, what is it that causes these electric cur-
rents ? If the tubes A and B of fig. 1 arc luted together without
any clay j)late between them, and a stream of water is passed
through them, no deflection is observable in the multiplier.
Hence it is seen that the presence of a diajihragm is necessary
for the manifestation of an electric current.
The law that obtains in all these experiments may be stated
concisely in these terms : —
458 Royal Society : —
The electromotive force which is developed when a certain pres-
sure forces pure irate)' through a clay plate, is independent of the
size and thickness of the plate, and also of the amount of ivater
that has flowed through, hut is proportional to the pressure em-
ployed.
The multipliers used for. these experiments were such as are
employed by M. E. du Bois-Reymond in his researches in organic
electricity. In one of the instruments the wire was wound no
less than 33,000 times round the frame, in the others 10,080
and 600 respectively.
In a subsequent Number of PoggendorfF^s Annalen (Part II
for 1859), M. Quincke announces that he has since discovered
that, by using flowers of sulphur as a porous diaphragm, the
electromotive force, all other circumstances remaining equal, is
incomparably greater ; and that this substance is therefore better
suited than burnt clay for forming a diaphragm-apparatus, so
that now there will be no further difficulty in demonstrating
these electrical currents under moderate pressures. The sulphur
which was mentioned in the original paper as being used for a
porous plate, was roll- sulphur ground to powder in an agate
mortar, as were also the talc and the graphite. At the close of
his supplementary notice, M. Quincke remai'ks that he has been
able to establish the two following facts with respect to these
electrical currents ; first, that they produce chemical decomposi-
tion ; and secondly, that they afford evidence of free electricity.
LXIII. Proceedings of Learned Societies.
ROYAL SOCIETY.
[Continued from p. 398.]
Dec. 8, 1859. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.
'T^HE following communications were read : —
■*- " Supplement to a Paper ' Oa the Influence of White Light, of
the different Coloured Rays, and of Darkness, on the Development,
Growth, and Nutrition of Animals*. By Horace Dobell, M.D. &c.
The apparatus used in the following experiments, was described in
my Paper ; but in the present instance, only two of the cells were
employed, viz. that exposed to ordinary white light, and that from
which all light is excluded. In order more effectually to prevent
the possible admission of light, the following precautions were adopted
with the dark cell: — 1. The perforated zinc floor was covered with
thick brown paper. 2. The under surface of the Ud was hned with
black cloth, to secure accurate adjustment when shut. 3. The
opaque black glass was covered with an additional coat of black oil-
paint. 4. The lid was never opened in any light except that of a
Candle or of gas.
* Phil. Mag. S. 4. vol. .xviii. p. 143.
Dr. Dobell on the Influence of Light on the Growth of Animals. 459
March 20th, 1859. — A number of ova of the Silkworm (Bomlyx
mori), all of the same age, were placed in each of the two cells. No
change was observed until Alai/ IHth (sixty days after the commence-
ment of the experiments), when one larva emerged from the ovum
in each cell ; and during twelve days, larvae continued to emerge in
the light and in the dark at the same rate.
June 9 th. — Sixteen larvse, as nearly as possible of the same size,
were selected in each cell, and the rest removed. The experiments
then proceeded with these thirty-two individuals, and no death
occurred from first to last.
The following Table shows the day on which each laiwa began to
spin ; the day on which the perfect insect escaped from the pupa ;
and hence the number of days occupied by the metamorphosis.
Light.
Darkness.
Day of
Day of
Number'of days
Day of
Day of
Number of days
beginning
escape of
occupied by meta-
beginning
escape of
occupied by meta-
to spin.
the Moth.
morphosis.
to spin.
the Moth.
morphosis.
July 1
July 18
18 days inclusive
June 30
July 18
19 days inclusive
„ 2
„ 19
18 „ „
„ 30
„ 18
19 „
.. 2
„ 19
18 „ „
„ 30
„ 18
19 „
„ 2
„ 18
17 „ „
„ 30
„ 18
19 „ „
.. 2
„ 18
17 „ „
» 30
„ 21
22 „
M 2
„ 19
18 „ „
July 1
„ 18
18 „
„ 2
„ 19
18 „ „
„ 1
„ 18
18 „ „
„ 3
„ 19
17 „ „
„ 2
„ 18
17 „ „
M 3
„ 21
19 ,, „
„ 2
„ 19
18 „ „
„ 4
„ 20
17 „
„ 2
„ 20
19 ,,
., 4
„ 20
17 „ „
,. 2
„ 19
18 „
M 4
„ 20
17 „ „
» 2
„ 20
19 „ „
,, 4
„ 21
18 „
„ 2
„ 21
20 „ „
„ 4
„ 21
18 „
,. 3
„ 21
19 „ „
» 5
„ 21
17 „
„ 3
„ 20
18 „
„ 6
„ 24
19 „ „
„ 4
„ 21 18 „ „
From this it is seen that the mean period occupied by the meta-
morphosis in the darkened cell was eighteen days fifteen houi's, and
in the liffht cell seventeen days sixteen hours.
The longest and shortest periods in the darkened cell twenty-two
days and seventeen days, in the light cell nineteen days and seven-
teen days.
June 9th. — On selection of sixteen of the largest larvae from the
inhabitants of each cell, it was noted that, when sixteen were selected
from the darkened cell and several of similar size removed, only
four could be found as large in the white cell, the remaining twelve
selected were therefore of a rather smaller size. This difference in
the two cells became less obvious afterwards, but, throughout the
experiments, there was a slight difference of size in favour of the
darkened cell.
With these exceptions, no difference could be detected between the
results obtained in the cell from wbich light was completely excluded
and in that exposed to its full influence.
The larvse, the silk produced, and the moths from the two cells.
460
Royal Society .
when placed side by side, coiUd not be distinguished from one
another.
The ova were of the same colour when first deposited, and under-
went the same changes of appearance, at the same time, in the dark
and in the light.
So far, therefore, as the direct agency of light is concerned in the
development, growth, nutrition, and coloration of animals, the results
of these experiments closely correspond with those already recorded
in my Paper.
" Supplement to a Paper ' On the Thermodynamic Theory of
Steam-engines with drv Saturated Steam, and its application to prac-
tice.' " By W. J. Macquorn Rankine, C.E., F.Pi.S. &c.*
This supplement gives the dimensions, tonnage, indicated horse-
power, speed, and consumption of fuel, of the steam-ships whose
engines were the" subjects of the experiments referred to in the
original paper. Results are arrived at respecting the available heat
of combustion of the coal employed, and the efficiency of the furnaces
and boilers, of which the following is a summary : —
No. of
experiment.
Kind of boiler.
; 1
i Available beat of i
Total heat of com- combustion of lib.! Available
bustion of 1 lb. of of coal in ft. -lbs. heat, total
coal in ft. -lbs , ; computed from heat, = eflS-
estimated from 1 efEciency of steam ciency of
chemical compo- and weight of ' furnace
sition. coal burned per and boUer.
I.H.P.
[
I-
III. 1
1
!
II.
r Improved Marine "1
< Boilers of ordi- >
[ nary proportions. J
'Boiler chiefly com-^
posed of small 1
vertical water- 1
j tubes, with very [
great heating
surface.
■ 10,000,000 5,420,000
! 10,000.000 5,200,000
1
; 1
i
' 11,560,000 : 10,110,000
i
0-542
0-53
0-88
Available Heat of Combustion of 1 lb. of coal
_ 1,980,000 ft.-lbs.
Efficiency of steam x lb. coal perl. H. P. per hour
"Researches on the Phosphorus-Bases." — No. VII. Triphospho-
nium-compounds. By A. W. Ilofmann, LL.D., F.R.S. Sec.
In several previous communications I have submitted to the Royal
Society the results which I have obtained in examining the deport-
ment of triethylphosphine with dibromide of ethylene, as the proto-
type of diatomic bromides. I have shown that the final product of
this reaction is a diatomic salt corresponding to two molecules of
chloride of ammonium.
The further prosecution of the study of triethylphosphine in this
direction has led me to investigate the derivatives generated by the
* Phil. Trans. 1839, p. 17/ ; and Phil. Mag. S. 4. vol. xviii, p. 71.
D. Hofmann on Triphosphonium-compounds. 461
phosphorus-base when submitted to the action of triatomic chlorides,
bromides, and iodides.
The most accessible terms of this group being cliloroform, bromo-
form, and iodoform, the changes of triethylphosphiue under the in-
fluence of these agents have more especially claimed my attention.
Action of Iodoform on Triethylphosphine.
Both substances unite with energy at the common temperature.
In order to avoid the inflammation of the phosphorus-base, small
quantities of the materials should be mixed at a time. The products
of the reaction vary with the relative proportions of the two sub-
stances.
By adding gradually crystals of iodoform to a moderate bulk of
triethylphosphiue until a new addition produces no longer an eleva-
tion of temperature, a viscous mass of a clear yellow colour is obtained,
which, when treated with alcohol, changes to a white powder of cry-
stalline aspect ; these crystals are easily soluble in water, difficultly
soluble in alcohol, and insoluble in ether. Two or three crystalliza-
tions from boiling alcohol render them perfectly pure. The analysis
of this body has led me to the formula
which represents a compound of one molecule of iodoform, and three
molecules of triethylphosphiue,
3C„H,P-fC,Hl3=C3jI,3P3l3.
Triethyl- Iodoform. New Compound.
phosphiue.
Iodoform thus fixes three molecules of triethylphosphiue, giving
rise to the formation of the tri-iodide of a triatomic metal, of a tri-
phosphonium corresponding to three molecules of chloride of ammo-
nium.
CTT p T
(CJI)
III
-I III
lP3
13.
(C.H3)3
(CJI,,)3
The aqueous solution of the iodide yields with iodide of zinc a
white crystalline precipitate which is difficultly soluble in water, and
appears to be slightly decomposed by recrystallization. It consists
of one molecule of the triatomic iodide and three molecidcs of iodide
of zinc, C,,!!,,?^!,, 3ZnI.
By treating the tri-iodide with the various salts of silver, a series
of triatomic compounds is easily obtained, which contain the different
acids.
The trichloride furnishes with dichloride of platinum a pale-yellow
precipitate, which is insoluble in water, but dissolves in boiling con-
centrated hydrochloric acid. From this solution it is deposited on
cooling in brilliant rectangular jjlates, which contain
C,, II ,„ P3 CI3, 3 Pt CI .
I have vainly tried to produce a trioxide which would correspond
to the tri-iodide.
The tri-iodide is promptly attacked by oxide of silver, with formation
of iodide of silver, and of an exceedingly caustic fixed base, which
remains in solution. This base no longer belongs to the same series.
462
Royal Society .
C„ R. PI=
By treating its solution with hydriodic acid, or with hydrochloric
acid and dicliloride of platinum, it is at once perceived that the action
of the oxide of silver has profoundly changed the original system of
"molecules. Hydriodic acid no longer produces the salt difficultly
soluble in alcohol ; by evaporating the solution a crystalline residue
is obtained, which easily separates into a viscous, extremely soluble
substance, and splendid crystals of an iodide, very soluble in water
aud alcohol, but insoluble in ether. The analysis of this iodide has
proved it to contain r-Q jj
C,H.
This formula represents the iodide of methyl-triethylphosphonium,
which was formerly obtained by M. Cahours and myself, by acting
with iodide of methyle upon triethylphosphiue.
The alkaline liquid, obtained by the action of oxide of silver upon
the tri-iodide, when saturated with hydrochloric acid, yields no longer
the platinum salt, difficultly soluble in water but soluble in hydro-
chloric acid. In a dilute solution no precipitate whatever takes
place, and only after considerable evaporation well-defined deep
orange-yellow octahedrons are deposited, which contain
C4H.
C,H.
From these results it is obvious ^tliat the triphosphonium-salt,
when submitted to the action of oxide of silver, passes over into a
monophosphonium-compound. The latter is not the sole product of
the reaction ; I have already alluded to the viscous deliquescent
substance which accompanies the iodide of methyl-triethylphospho-
nium. This is an iochde which, in the solution produced by the
action of oxide of silver upon the original tri-iodide, exists in the form
of oxide. The latter substance is easily recognized by evaporating
the solution of oxide of methyl-triethylphosphonium, and adding a
concentrated solution of potassa, w hen the oily globules characteristic
of the dioxide of triethylphosphonium separate, which disappear
immediately on addition of water.
The metamorphosis of the tri-iodide, under the influence of oxide
of silver, is represented by the following equation : —
C.^H^gPCl, PtCl,=
CI, Pt CL
-(C,H)"'
(C.H,)3
(C,H,),
.(C.H,)3
J
l3 + 3AgO-F3HO=:3AgI +
0, + 2
The tri-iodide which forms the subject of this Note is not the only
product of the reaction between iodoform and triethylphosphiue.
There are other compounds formed, especially when the iodoform is
employed in great excess. The nature of these bodies, which may
be divined from the examiuatiou of the corresponding compounds m
the diatomic series, is not yet fixed by experiment.
Prof. Powell : Comparison of Refractive Indices with Theory. 4fi3
I have satisfied myself that chloroform and bromoform act like
iodoform upon tiiethylphosphine.
The phosphorus-base acts, even at the common temperature, upon
tribromide of allyle. The mixture of the two bodies solidifies into a
crystalline mass, in the examination of which I am engaged.
The reactions which I have pointed out in this Note have induced
me to extend my experiments to tetratomic bodies. The chloride of
carbon, C.Cli, obtained by the .final substitution of chlorine for the
hydrogen in marsh-gas, appeared to promise accessible results. On
submitting this body, remarkable for its great indifference under
ordinary circumstances, to the influence of triethylphosphine, I have
observed with astonishment a most powerful reaction. Every drop
of triethylphosphine which is poured into the chloride of carbon,
hisses like water falling upon red-hot iron. On cooling, the mixture
solidifies into a mass of white crystals, which will be the subject of a
special communication.
December 1.5. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair.
The following comniunication was read : —
" Comparison of some recently determined Refractive Indices with
Theory." By the Rev. Baden Powell, M.A., F.R.S. &c.
In a series of papers inserted in the Philosophical Transactions
(1835, 1836, 1837), and afterwards, in a more correct and complete
form, in my Treatise * On the Undulatory Theory applied to the Di-
spersion of Light' (1841), I endeavoured to investigate the great
problem of the explanation of the unequal refrangibility of light on
the principles of the undulatory theory, as proposed by M. Cauchy
about 1830, by numerical comparison with the indices observed,
more especially in cases of the most highly dispersive media then
examined.
The general result then arrived at was, that while the theory
applied perfectly through an extensive range of media of Ioav and
moderate dispersive power, it did not apply well to those of higher ;
and to the highest in the scale (which of course formed the true
test of the theory) it did not apply within any allowable limits of
accuracy. Since that time little has been done towards prosecuting
the subject.
In the experimental part of the inquiry, about 1849, I had ob-
served the indices for a few new media* ; but these were not hio-h in
the scale ; yet though perhaps thus of little importance, I have now
thought it as well to go through the calculation for them : the
results are of the same general character as just described.
Soon after, finding that my friend, the Rev. T. P. Dale, F.R.A.S.,
was desirous to carry on some researches of this kind, I placed
at his disposal tlie apparatus with which I had determined all my
indices f.
In 1850 that gentleman communicated to the Royal Astronomical
Society a short general account of his observations % relative to some
substances not very high in the scale.
* See British Association Reports, 1850, Sect. Proc. p. 14.
t Described and figured, Britisli Association Reports, 1839,
X Notices, vol. xi. p. 47.
464 Royal Society : —
In 1858, Mr. Dale, in conjunction with Dr. J. H.Gladstone, F.R.S.,
presented to the Royal Society* a valuable series of determinations,
evincing highly interesting results relative to the change of refractive
power in various substances under different temperatures.
None of these media being high in the scale, they have little
bearing on the main object of my inquiries. In two cases (viz. water
and alcohol) the indices agree so closely with mine, that it was not
worth while to recalculate them. In two other cases I have carried
out the numerical comparison, which affords a good agreement with
the theory.
Very recently the same gentlemen have, however, published some
observations on several other media, especially phosphorus, a sub-
stance at the very summit of the scale, for which I had long been
extremely desirous to obtain some determinations of indicesf.
Among these results only two sets are in a form in which they can
be made available for comparison with theory. These are the indices
for the standard rays in bisulphide of carbon, and for solution of phos-
phorus in that medium, which I have now calculated theoretically.
The results (given in the sequel) in both cases indicate discre-
pancies between theory and observation too great to be due to any
reasonable allowance for error ; and we are confirmed in the con-
clusion before arrived at, that, for highly dispersive substances, the
theory, in its present state, is defective.
But these comparisons are all made by means of the same formula
employed in my former researches, viz. that derived from Cauchy's
theory by Sir W. R. Hamilton, which he communicated to me, and
which I explained in a paper in the Philosophical Magazine ;f.
Considering the unsatisfactory condition in which the question
was left when tried by the test of the higher media in my former
inquiries, it is a matter of some surprise that in the long interval
since the publication of those results no mathematician has been in-
duced to revise the theory. Some criticisms indeed were advanced
by Mr. Earnshaw§, and others by Prof. Mosotti and the Abbe
Moignoll, bearing on the general principle. Sir W. R. Hamilton's
formula in particular was founded on certain assumptions con-
fessedly but app)-oxitnate. It remains then a promising field for
inquiry to analysts, whether a better formula might not be deduced,
or other improvements made in tbe general theory, by which a
method applying so well to lower cases might be made equally
successful for the higher.
Results of calculation, /or Ether, Hydrate of Phenyle, Oils of Spike-
nard, Lavender and Sandal-wood, Benzole, Bisulphide of Carbon,
and Solution of Phosphorus in that medium.
Three indices assumed from observation, viz. /u , ^ and n , give
the medium constants, viz.
* Phil. Trans. 1858. f See Phil. Mag. July 1859.
+ Vol. viii. N. S. March 1836. § Sec Phil. Mag. April 1842 and August 1842.
II See British Association Reports, 1849, Sect. Proc. p. 8.
Prof. Powell : Comparison of Refractive Indices with Theory. 465
The values of the wave-length constants A and B for each ray,
independent of the medium, are taken from my Treatise (Undulatory
Theory applied to Dispersion, &c.. Art. 270). Combining these, we
obtain Al) and BD' for each ray in the medium.
Thence Sir W. R. Hamilton's formula {ib. Art. 237) gives for any
''^y* /u=/xf± (AD + BD');
the upper sign being used for rays above F, the lower for those below.
Ether. — Dale and Gladstone.
Ray.
A'-
Difference.
Observation.
Theory.
B
C
D
E
F
G
H
1-3545
1-3554
1-3566
1-3590
1-3606
1-3646
1-3683
1-3544
1-3566
1-3586
1-3646
--0010
-•0000
--0004
-0000
1
Hydrate of Phenyle. — Dale and Gladstone.
B
C
D
E
F
G
II
1-5416
1-5433
1-5488
1-5564
1-5639
1-5763
1-5886
1-5428
1-5495
1-5567
1-5772
--0005
+ •0007
I +-0003
+ •0009
i
In both these media, of low dispersive and refractive power, the
accordances of theory and observation are sufficiently close.
Oil of Lavender. — Powell.
B
r464I
1
C
r4658
i 1-4632
-•0026
D
1-4660
1 1-4678
+ •0018
E
1-4728
1 r4726
--0002
F
1-4760
'
G
1-4837
1-4848
+ -00 11
H
1-4930.'
1
Oil of Sandal-wood. — Powell.
B
1-5034
C
1-5058
1-4988
--0070
D
1-50.Q1
1-5062
— •0029
E
1-5117
1-5102
— •0015
F
1-5151
G
1-5231
1-5271
+ •0040
H
1-5398?
466
Royal Society : —
Oil of Spikenard. — Powell.
Ray.
Z^-
Difference.
Observation.
Theory.
B
C
D
E
F
G
H
1-4732
1-4746
1-4783
1-4829
1-4868
1-4944
1-5009
1-4744
1-4082
1-4826
1-4945
--0002
--0001
-•0003
+ •0001
Benzole . — Powell.
B
C
D
E
F
G
H
1-4895
1-4981
1-4978
1-5041
1-5093
1-5206
1-5310
1-4907
1-4965
1-5029
1-5210
--0054
— -0013
— -0012
+ -0004
In oil of lavender and of sandal-wood there was some indistinct-
ness in the line H which renders its index a little uncertain. It may
be owing to this circumstance that the assumption of that index may
have occasioned the discrepancy between theory and observation.
In oil of spikenard the accordance is good. In benzole the discre-
pancies are too great.
Bisulphide of Carbon. — Dale and Gladstone.
Ray.
M-
Difference.
Observation.
Theory.
B
C
D
E
F
G
H
1-6177
1-6209
1-6303
1-6434
1-6554
1-6799
1-7035
1-6169
1-6251
1-6425
1-6807
— -0040
— -0052
--0009
+ •0108
Phosphorus dissolved in Bisulphide of Carbon.—
Dale and Gladstone.
B
1-9314
C
1-9298
D
\-ro27
1-9522
--0005
E
\-97AA
1-9726
-•0018
F
1-9941
G
2-0361
2-0363
+ •0002
H
2-0746
Geological Society. 467
In the first of these media the differences are greater than can be
fairly allowed to errors of observation.
In the second case it is yet more clearly apparent that the theory
is defective. The ray C was not observed ; but the theoretical index
is evidently in error to a large amount, as it is even lower than that
of B, The indices for D and C are perhaps within the limits of
error ; but that of E is too much in defect to be allowed.
GEOLOGICAL SOCIETY.
[Continued from p. 402.]
March 28, 1860. — L. Horner, Esq,, President, in the Chair.
The following communications were read : —
1. "Notes about Spitzbergen in 1859." By James Lament,
Esq., F.G.S.
Mr. Lamont cruised about the southern coasts of Spitzbergen in
his yacht during the summer and autumn of 1859. He first visited
Edge's Land, which is composed of horizontal strata of limestone,
shale, and sandstone, with some coal. One of the glaciers on
this coast has a frontage of 30 miles. Deeva Bay was explored
throughout. Black Point yielded some Carboniferous fossils. The
Thousand Isles are composed of greenstone, sometimes columnar.
Stour Fiord and Walter Thymen's Straits were next visited. The
shores consist of the same kind of horizontal strata, with trap-rocks.
Bell Sound and Ice Sound on the west coast, were also examined ;
the former has high hills of grey fossiliferous Hmestone all round it ;
the fossils, as determined by Mr. Salter, prove to be all Carboni-
ferous. At various points on the coast and islands of southern
Spitzbergen Mr. Lamont found bones of whales at elevations of 10
to 100 feet above the sea, and at distances of from a few yards to
half a mile inland. The bones are sometimes imbedded in banks
or moss. Drift-wood (pine) also abounds ; some of it lies 30 feet
above high-water-mark.
In the supplement to this paper, Mr. Horner supphed a descrip-
tion of the rock-specimens brought from northern Spitzbergen by
Parry and Foster in 1827. From the evidence thus aflforded it
appears that the islands and mainland about the entrance of Waigatz
Straits consist of granitic and gneissic rocks with quartz-rock and
crystalline Hmestones, — possibly the altered equivalents of the
Carboniferous sandstones and limestones of southern Spitzbergen.
A list of the recent shells sent by Mr. Lamont from Spitzbergen
was supplied by Mr. Woodward. Prof. Huxley gave the result of
his examination of the bones — chiefly whale, white whale, and
walrus. Mr. Prestwich described the gravels from Bell Sound —
which consist chiefly of claj'-slate, hornblende-slate, and mica-slate.
Lastly Mr. Salter determined the following fossils — from the grey
limestone of Bell Sound, Athyris or Spirifer, a large species,
Productus costatiis, P. Humboldtii, P. tnanima/its and another species
of Productus, Camarophoria, Spirifer Keilhavii, Streptorhynchus
crenistria, Zaphrentis ovibos, Stenopora, Syringopora, Fetiestella,
specimens of a new genus allied to the last, and some Sponges ; —
from the dark-coloured limestone of Black Pomt, Edge's Land,
468 Intelligence and Miscellaneous Articles.
Nucula, a small Aviculo-pccten, and Spirifcr. A large Aviculo-
pccten probably from the same locality also occurs ; and one
weathered block of white limestone, perhaps from Bell Sound, yields
Spirifer alatus, a small Productus like the P. horridus figured by
De Koninck as brought from Spitzbergen by M. Robert, and a large
foliaceous Stenopora. These last, with a specimen of Spirifer
cristatus, on another loose block, are the only forms having a
Permian aspect in the collection made by Mr. Lamont.
2. " On the so-called Wealden Beds at Linksfield, and the
Reptiliferous Sandstones of Elgin." By C. Moore, Esq., F.G.S.
When visiting the section at Linksfield, near Elgin, in the
autumn of 1859, the author recognized a similarity of appearance
between the shales and thin limestone-bands at Linksfield and those
of the Bone-bed series (at the base of the Lias) at Pylle Hill, near
Bristol, at Aust Passage and at Penarth, on the Severn, and at the
Uphill cutting on the Great Western Railway. Giving in detail
the sections at Pylle Hill and at Linksfield, the author pointed out
some close lithological resemblances, and stated that he recognized
the " white lias," the " Gotham marble," the " bone-bed," and the
gypseous clay-bands of the south in the quarry at Linksfield.
Cyprides, Estherice, remains of Hxjhodus, Lepidotus, Acrodus, and
Plesiosaurus, Mytilus, Modiola, Unio, and Cyclas, from the Links-
field beds, were among the palaeontological evidences which the
author brought forward as supporting his correlation of the beds in
question.
He next offered some observations on the red layer of clay, sand,
and stones intercalated between the Linksfield shales and the corn-
stone, and, not accepting Capt. Brickenden's opinion of its having
been thrust in by the action of ice against the escarpment during
the formation of the boulder-clay, he suggested that an early glacial
period, contemporaneous with the Lower Lias, destroyed some of
the lower shales and limestone of Linksfield, leaving their remnants
imbedded in a red drift to be covered by the succeeding undis-
turbed deposits of the bone-bed series.
Mr. C. Moore next remarked that the Cornstone at Linksfield,
on which all the above-mentioned beds rest, might possibly be of
Triassic date, as he had observed on the flanks of the Mendips and
elsewhere a stone of a similar aspect, belonging to the Trias, and
occasionally yielding remains of Reptiles and Fishes ; to this rock the
author refers the druidical stones of Stanton Drew. Some observa-
tions on the discovery of reptilian and mammalian teeth in a Triassic
deposit near Frome, by the author, on the possible relations of
some of these to the Reptilia found in the Lossiemouth sandstone,
and on the probable Secondary age of the latter, concluded the paper.
LXIV. Intelligence and Miscellaneous Articles.
NEW SECONDAKV PILE OF GREAT POWER. BY M. G. PLANTE.
JACOBI proposed recently the use of secondary electric currents for
telegraphic purposes, and Plante had suggested the substitution
of electrodes of lead for those of platinum in these batteries. A more
Intelligence and Miscellaneous Articles. 4G9
extended study has convinced him of their use. He states that
a battery with electrodes of lead has 2h times the electromotive
force of one with electrodes of platinized platinum, and six times as
great as that of one with ordinary platinum. This great power arises
from the powerful affinity which peroxide of lead has for hydrogen,
a fact first noticed by De la Rive. The secondary battery which he
recommends has the following construction. It consists of nine
elements, presenting a total surface of ten square metres. Each
element is formed of two large lead plates, rolled into a spiral
and separated b}' coarse cloth, and immersed in water acidulated
with one-tenth sulphuric acid. The kind of current used to excite
this battery depends on the manner in which the secondary couples
are arranged. If they are arranged so as to give three elements of
triple surface, five small Bunsen's cells, the zincs of which are im-
mersed to a depth of seven centimetres, are sufficient to give, after a
few minutes' action, a spark of extraordinary intensity when the
current is closed. The apparatus plays, in fact, just the part of a
condenser ; for by its means the work performed by the battery, after
the lapse of a certain time, may be collected in an instant. An idea
of the intensity of the charge will be obtained by remembering that
to produce a similar effect it would be necessary to arrange 300
Bunsen's elements of the ordinary size (13 centimetres in height),
so as to form four or five elements of 3^ square metres of surface,
or three elements of still greater surface. If the secondary battery
be arranged for intensity, the principal battery should be formed
of a number of elements sufficient to overcome the inverse electro-
motive force developed. For nine secondary elements about fifteen
Bunsen's cells should be taken, which might, however, be very small.
From the malleability of the metal of which it is formed, this battery
is readily constructed ; by taking the plates of lead sufficiently thin,
a large surface may be placed in a small space. The nine elements
used by Plante are placed in a box 36 centimetres square, filled with
liquid once for all, and placed in closed jars ; they may also be kept
charged in a physical cabinet, and ready to be used whenever it is
desired to procure, by means of a weak battery, powerful discharges
of dynamic electricity. — Comptes Rendits,^ldirch. 26, I860.
NOTE ON THE USE OF SULPHATE OF LEAD IN VOLTAIC COUPLES.
M. Edm. Becquerel describes a modification of the sulphate of
lead battery invented by his father, iM. Becquerel.
Sulphate of lead has the property, when it is made into a paste
with a saturated solution of chloride of sodium, of becoming hard
and compact ; other chlorides exert a similar action. (Cylinders may
be moulded of this paste, if a rod of copper, lead, tin-plate, or
even of gas-coke be placed in the centre. These cylinders, when dry,
are permeable to a liquid conductor in which they are placed, and in
contact with zinc form a constant current. Plates may also be
formed of this substance ; and when placed at the bottom of a vessel
resting on a conducting su])port of copper, lead, or tin-plate, a piece
of zinc being suspended above them, and the vessel filled with aci-
Phil. Mag. S. 4, Vol. 19. No. 129. June 1860. 2 I
470 Intelligence and Miscellaneous Articles.
dulated water or solution of chloride of sodium, a constant couple
with a single liquid is formed, without a diaphragm. But usually
the cylindrical form, combined with the use of a cloth or porcelain
diaphragm, is preferable.
AH samples of sulphate of lead are not alike, probably from the
presence of foreign admixtures ; some become very hard, others do
not acquire a sufficient resistance. Without knowing on what this
depends, a mixture of 100 grammes of dried and pounded sul])hate
of lead, 20 to 30 grammes of chloride of sodium, and 50 cubic centi-
metres of saturated solution of chloride of sodium, gives good re-
sults : the addition of 20 to 25 grammes of oxide of lead (minium
or massicot) increases the hardness of the mass. Another method
of using the different sulphates of lead is perhaps preferable. It
consists in coating the freshly moulded sulphate of lead with a thin
layer of plaster. This mass being placed in a liquid in the interior
of a hollow zinc cylinder, constitutes a couple ; in this way the sul-
phate does not get out of shape, nor is there any necessity for a
diaphragm ; the plaster serves this purpose, and prevents the con-
tact of the zinc and the reduced lead.
In these couples either water acidulated with sulphuric acid, or
solution of chloride of sodium may be used ; in the latter case the
electromotive force is somewhat greater than in the former, but the
solubility of sulphate of lead in it causes a deposition of reduced lead
on the zinc, which must be removed from time to time. With
acidulated water this is not the case.
The electromotive force of these new couples, as compared with
that of a zinc-platinum couple, water containing one-tenth of acid,
and nitric acid, is as follows : —
Couple witli nitric acid 100
Couple with sulphate of copper 58 to 59
-^ , . , r With solution of chloride of
Couple with compact per- ^^^,j^^ 28 to 30
meable sulphate of lead ^^,.^^ ^^.^^^^ acidulated with
and amalgamated zinc i i • • i o7
" 1^ sulphuric acid 27
In the first moments of the action the electromotive force de-
pends on the nature of the conductor in contact with the sulphate
of lead ; but as soon as there is metallic lead reduced, it attains a
constant value. When these couples are in operation, the sulphate
of lead is reduced to the metallic state — the sulphuric acid from it
forming sulphate of zinc : the lead may be obtained by fusion.
From the chemical equivalents we readily get the relative weights
which the two electrodes must possess in order to have a constant
current; 100 grammes of zinc require 4 70 grammes of sulphate of lead.
These solid masses, permeable to liquids and employed as negative
electrodes, by preventing polarization play the same part as the per-
oxides of lead or manganese, nitric acid, and reducible metallic salts ;
but their resistance to conductibility, which varies with the progress
of the reduction, prevents the apijlication of these couples with a
single liquid to the same uses as nitric acid couples. They may,
however, be used with advantage where piles of great resistance
and long duration are required. — Comptes Rendus, April 2, 1 860.
471
INDEX TO VOL, XIX.
Abel (F. a.) on the composition of
water from the coal-strata of York-
shire, 330.
Acetone, researches on, 110.
Actinoraeter, description of a new, 39.
Alcohol, on the electric deportment of
the flame of, 9.
Alcohols, on new, 209.
Aldehydes, on the behaviour of the,
with acids, 309.
Allomerism, observations on, 405.
Alloys, on the conductibiUty of cer-
tain, for lieat and electricity, 243.
Aluminium-leaf, on the preparation
and properties of, 280.
Angle, on a new instrument for the
mechanical trisection of an, 261.
Animals, on the influence of white
light on the growth of, 458.
Antimony, amorphous, on the specific
gravity of electro-deposited, 403.
Arseniates, on the production of some
native, 380.
Arsenious acid, on the effects produced
by the administration of, 214.
Athamantine, on a nitro-compound
of, 51.
Atkinson's (Dr. E) chemical notices
from foreign journals, 48, 116, 20/,
277, 380.
Atmosphere, on the vertical currents
of the, 421.
Babington (Dr. B. G.) on spontaneous
evaporation, .314.
Barometers, on the construction of
new forms of, 1.
Battery, on the construction of a new,
of great power, 468.
Bechamp (M.) on the preparation of
l)ermanganate of potash, 383.
Bccqucrcl (M.) on the use of insoluble
compounds in voltaic batteries, 404 ;
on a sulphate of lead battery, 469.
Berthelot (M.) on some new alcohols,
209.
Bineau (M.) on the determination of
the densities of superheated vapours,
208.
Bohn (M.) on the optical properties
of artificial tartaric acid, 126.
Books, new : — Winter's Geometrical
Drawing, 148.
Boracic acid, on the occurrence of, in
the sea-water on the coast of Cali-
fornia, 323.
Bunsen (Prof.) on the chemical action
of light, 61.
Bussenius (M.) on a rock oil obtained
from some lias shales neai* Ha-
nover, 389.
Calcite, on some prismatic forms of,
333.
Carius (M.) on the equivalent substi-
tution of oxygen by sulphiu", 283.
Cartmell (R.) on the behaviour of the
aldehydes «ith acids, 309.
Cavaileri (P. G. M.) on a new seis-
mometer, 102.
Challis (Prof.) on the possibility of
finding a root of ever}' equation, 46;
on a theory of molecular forces, 88.
Chancel (M.) on the determination of
phosi)horic acid, 381.
Chemical notices from foreign jour-
nals, 48, 116, 207, 277, 380.
Chinovine, researches on, 50.
Chlorous acid, on oxidation by, 120.
Chromium, on the nitride of, 278.
Clausius (Prof.) on the dynamical
theory of gases, 434.
Cloez (M.) on some new benzoic
compounds, 282.
2 12
4.72
INDEX.
Coal, on the occurvence of, in the
chalkof Kent, 318.
Cockle (J.) on the theory of equations
of the fifth degree, 197, 331.
Colour-blindness, remarks on, 148.
Cooke (Prof. J. P.) ou the possible
variation of constitution in a mineral
species independent of the pha;no-
mena of isomorphism, 405.
Corvisart (M.) on the action of light
upon amylaceolis substances, 281.
Crystallographic notices, 325.
Crystals, on the measure of the dihe-
dral angles of, 328.
Cyaphenine, on the preparation and
composition of, 283.
Davy (Dr. E. W.) on a simple and
expeditious method of estimating
phosphoric acid, 181.
Davy (Dr. J.) on the electrical con-
dition of the egg of the common
fowl, 55.
Dawson (Dr. J. W.) on some fossils
from the coal-formation of Nova
Scotia, 159.
Debray (M.) on the production of na-
tive ])hosphates and arseniates, 380.
Deraidoffite, on the composition of,
14.
Deville (M.) on the specific gravities
of certain vapours at high tempe-
ratures, 207.
Diabetes, on lesions of the nervous
system producing, 52.
Dispersion, chromatic, on certain laws
of, lfi5, 2(i3, 364.
Dobell (Dr. H.) on the influence of
light on the growth of animals, 458.
Donkin (Prof.) on the theory of the
attraction of solids, 397.
Dufour (C.) on the scintillation of the
stars, 216.
Earnshaw (Rev. S.) on the velocity of
sound, 449.
Earth, on the thickness of the crust
of the, 274,34:5, 444.
Egg, on the electrical condition of
the, 55.
Eisenstiick (M.) on a rock oil obtained
from some lias shales near Ha-
nover, 389.
Eissfeldt (M.) on pyrocatcchine, 51.
Electric current, on a new kind of,455.
deportment of the flame of alco-
hol, on the, 9.
light, on the, 320.
Electrical conductivity, researches on,
14.
discharge in vacuo, experiments
on the, 59 ; on the influence of
magnetic force on the, 238.
Electrode, on the behaviour of mer-
cury as an, 1 29.
Ellis (A. J.) on the systematization of
mathematics, 224.
Equation, on the proposition that
every, has a root, 46.
Equations of the fifth degree, on the
theory of, 197, 272, 331.
Ericinone, on the preparation and pro-
perties of, 51.
Espenschied (M.) on nitride of sele-
nium, 277.
Ethylamine, on new derivatives of,
232.
Ethylene, on some combinations of
the oxide of, with ammonia, 125;
on the action of, on chloride of sul-
phur, 388.
Evaporation, on spontaneous, 314.
Faraday (Prof.) on hghthouse illumi-
nation, 320.
Fittig (M.) on several processes of
decomposition of acetone, 116.
Fizeau (H.) on the effect of the mo-
tion of a body upon the velocity
with which it is traversed by light,
245.
Flames, on the composition of the
gas in non-luminous, 121.
Forces, on the coiTelation of, 133,
243.
Fossils, descriptions of new, 159.
Foucault (M.) on the simultaneous
emission and absorption of rays of
the same refrangibility, 193.
Fraunhofer's lines, observations on,
193.
Fraxetine, on the constitution of, 49.
Gases, on the dynamical theory of,
19, 434.
Gassiot (J. P.) on the electrical dis-
charge in vacuo, 59.
Geikie (A.) on the old red sandstone
of the south of Scotland, 237.
Geological Society, proceedings of
the, 75, 158, 235, 318, 399, 467-
Geuther (A.) on the behaviour of the
aldehydes with acids, 309.
Gej'ger (M.) on the constitution of
athamantine, 51.
Gilm (Von) on chinovic acid, 50.
I N D E X.
473
GI3 col, on the action of acids ou, (iU ;
on new derivatives of, 1 22.
Gore (G.) on the specific gravity of
electro-deposited amorphous anti-
mony, 403.
Granites, ou the origin of, 32.
Greg (R. P.) on several new British
minerals, \3; on luminosity of
meteors from solar rellcxiou, 287.
llankel (W. G.) ou the electric de-
portment of the tlame of alcohol, V.
Ilarkness (Prof. R.) ou the metamor-
phic rocks of the Grampians, 236.
Haughton (Prof. S.) on the thickness
of the crust of the earth, 343, 444.
Hearder (J. N.) on electrical conduc-
tivity, 14.
Heat, on the transmission of radiant,
through gaseous bodies, 60 ; ou the
interference of, 126 ; engendered
by the fall of a meteor into the sun,
on the, 338.
Heinz (Dr.) on two new series of acids,
385.
Helmholtz (M.) on vowel sounds, 81.
Hennessy (Prof. H.) on vertical cur-
rents of the atmosphere, 421.
Herschel (Sir J. F. W.) on colour-
blindness, 148.
Hinton (J.) on the correlation of force,
243.
Hippuric acid, on new derivatives of,
119.
Hlasiwetz (M.) on quercitrine, 48; on
chinovine, 50.
Ilofmann (Dr. A. W.) on new deri-
vatives of phenylamine and ethyl-
amine, 232 ; on phosphammonium
compounds, 306 ; on triphospho-
nium compounds, 460.
Ice, ou some properties of, at or near
its melting-point, 3iM.
Jamin (J.) on the equilibrium and mo-
tion of liquids in porous bodu's,2()4.
Jellett (Rev. Prof.) on the controversy
between Archdeacon Pratt and Prof.
Haughton, 3-J3.
Jerrard (G. B.) on the theory of
quintics, 272.
Jones (T. R.) on recent and fossil
Foraminifera from the ^lediterra-
nean area, 161.
Kirchliotf (Prof.) on the simultaneous
emission and absorption of rays of
the same refrangiliility, ]'>3.
Kiiobluuch (Prof.) on the interference
of heat, 126; on some optical lec-
ture ex])erniients, 162.
Kolbe (Prof.) on the synthesis of sali-
cylic acid, 212.
Lactic acid, on the preparation of, 385,
Lainont(Dr.) on j)h;enomena observed
during total eclipses of the sun,
416.
Lamont (J.) on the geology of Spitz-
bergen, 467.
Lautemann (M.) on the synthesis of
salicylic acid, 212; on the forma-
tion of propionic acid, 384 ; on the
preparation of lactic acid, 385.
Lead, ou a carbonate of, from leaden
coffins, 291 ; ou a new method of
separating from baryta, 383.
LeConte (Prof. J.) on the correlation
of forces, 133.
Le Roux (M.) on ozone, 403.
Leucine, on the occurrence of, in the
pancreas, 213.
Liebig (Prof.) on the formation of
tartaric acid from milk-sugar, 390.
Light, on the chemical action of, 61 ;
on the action of, upon chloride of
silver, 186; on the simultaneous
emission and absorption of rays of,
193 ; on the aberration of, 245 ; on
the action of, upon amylaceous sub-
stances, 281 ; on the influence of,
on the growth of animals, 458 ; on
the undulatory theory of, 463.
Liquids, on the equilibrium and mo-
tion of, in porous bodies, 204.
Lowe (M.) on the separation of lead
and baryta, 383.
Loureufo (M.) on new derivatives of
glycol, 122.
Lunge (M.) on the composition of the
gas in the dark cone of the non-
luminous flame of Bunsen's gas-
burner, 121.
JIagnesia, on the estimation of, 382.
Magnetic image, on the fixation of the,
KM.
force, on the influence of, on the
electric discharge, 23!>.
Mallet (Prof. J. W.)on osmious acid,
and the position of osmium in tiic
list of elements, 293,
Mathematics, on tlie laws of oyieration,
and the systematization of, 224.
Maxwell (Prof. J. C.) on the motions
and collisions of iH-rfectiy clastic
spheres. 1!'.
474'
INDEX.
Mdde (F.) on a new kind of sounil-
fijzures, 324.
Mevcnrv, on tlie behaviour of, as an
electrode, 12!).
Metals, on the relative conducting
power of, 15.
Meteor, on the heat engendered by the
possible fall of a, 338.
Meteors, on luminosity of, from solar
reflexion, 287.
Miller (Prof. W. H.), crystallographic
notices by, 325.
Minerals, on several new, 13, 78.
Moller (M.) on vulpic acid, 211.
Molecular forces, theory of, 88.
Moore (C.) on the reptiliferous sand-
stones of Elgin, 4()8.
Nickles (J.) on the fixation of the
magnetic image, 164.
Niemann (M.) on the action of ethy-
lene on chloride of suli)hur, 388.
Niepce de St. Victor (M.) on the
action of light upon amylaceous
substances, 281.
Niobium, on a new mitieral contain-
ing, 78.
Optical lecture-experiments, on some,
162.
Osmium, on the physical relations of,
293.
Owen (Prof.) on some remains of
Polyptychodon, 158.
Oxacetic acid and derivatives, 386.
Oxalan, on the formation and con-
stitution of, 285.
Ozone, on the production of, 403.
Parker (W. K.) on recent and fossil
Foraminifera from the Mediter-
ranean area, 161.
Pavy (Dr.F. W.) on lesions of the ner-
vous system producing diabetes, 52.
Percussion of bodies, on the, 430.
Permanganate of potash, on the pre-
])aration of, 383.
Petrol, on the preparation and pro-
perties of, 389.
Phenylamine, on new derivatives of,
232.
Phillips (Dr. J.) on some sections of
the strata near Oxford, 235.
Phloroglucine, on the constitution of,
50.
Phosphammonium compounds, re-
searches on the, 306.
Phosphates, on the artificial produc-
tion of some native, 380.
Phosjilioric acid, on new methods of
estimating, 181, 381.
Photochemical researches, 61.
Photogra])hic image, on the com-
position of the, 186.
Pinakone, on the preparation and
properties of, 1 1 9.
Plante (G.) on a new secoudui-y pile
of great power, 468.
Poinsot (M.) on the percussion of
bodies, 430.
Polyptychodon, on some remains of,
158.
Ponton (M.) on certain laws of chro-
matic dispersion, 165, 263, 364 ; on
the law of the wave-lengths cor-
responding to certain points in the
solar spectrum, 43/.
Potyka (Dr. J.) on a new mineral
containing niobium, 78.
Powell (Rev. B.) on some recently
determined refractive indices, 463.
Pratt (Archdeacon) on the solidity and
fluidity of the mass of the earth,
274, 343.
Propionic acid, on the formation of,
384.
Pseudo-diascope, description of the,
79.
Pyrocatechine, on the formula of, 51.
Quercitrine, on new derivatives of,
48.
Quincke (G.) on a new kind of electric
current, 455.
Quintics, on the theory of, 197, 272,
331.
Rankine (W. J. M.) on the thermo-
dynamic theory of steam-engines,
460.
Rays of same refrangibility, on the
simultaneous emission and absorp-
tion of, 193.
Rochleder (Dr.) on fraxetine, 49.
Roscoe (Prof.) on the chemical action
of light, 61.
Rose (Prof. 11.) on the diff"erent states
of silicic acid and the origin of
granites, 32 ; on a new method of
decomposing silicates, 382.
Royal Institution, proceedings of the,
238, 320.
Royal Society, proceedings of the, 52,
14^, 224, 306, 391,468.
Rutile, on the cleavages of, 329.
Salicylic acid, on the synthesis of.
212.
INDEX.
4-7.5
Scheerer (Prof.) on the estimation of
magnesia, .382.
Scherer (Dr.) on xanthine and leu-
cine, 213.
Schiel (Dr.) on the action of chlorous
acid on various organic substances,
120.
Schmidt (Prof.) on the action of
arsenious acid when introduced into
the circulation, 214.
Schonbein (Prof.) on the action of
platinum-bliick on j)eroxide of hy-
drogen, 280.
Schwanert (M.) on derivatives of
hippuric acid, 11.9.
Seismometer, description of a new,
102.
Selenium, on the nitride of, 277.
Silicates, on a new method of decom-
posing, 382.
Silicic acid, on the different states of,
32.
Silver, on the action of light on the
chloride of, 186.
Simpson (Dr. M.) on the action of
acids on glycol, 69.
Sonorous undulations, on the mode of
transmission of, in the human ear,
56.
Sound, on the velocity of, 449.
figures, on a new kind of, 324.
Spectra of coloured flames, experi-
ments on the, 193.
Spectrum, on the law of the wave-
lengths corresponding to certain
points in the solar, 437.
Spheres, on the motions and collisions
of perfectly elastic, 19.
Spiller (J.) on the composition of the
photographic image, 186.
Spratt (Capt ) on the freshwater de-
posits of Bessarabia, 160.
Stadelcr (G.) on the occurrence of
urea in the organs of the Plagi-
ostomous fishes, 79 ; on acetone,
118.
Stars, instructions for the better ob-
servation of the scintillation of, 216.
Steam-engines, on the thermo-dyna-
mie theory of, 460.
Stereogra])hic projection of the sphere,
on the employment of tlu', in cry-
stallography, 325.
Strecker (Dr.) on vul])ic acid, 211;
on new derivatives of alloxan, 2S6.
Stiirzwage (Dr.) on the eftVcts pro-
duced by the administration of
arsenious acid, 214.
Sullivan (Prof. W. K.) on some pris-
matic forms of calcite, 3.33.
Sulphur comj)ounds, on new, 283.
Sun, on a mode of deducing the
absolute temperature of the sur-
face of the, 3.38 ; on phtcnomena
observed during total eclipses of
the, 416.
Tartaric acid, on the optical proper-
ties of artificial, 1 26 ; on the forma-
tion of, from milk-sugar, 3!i0.
Tate (T.) on the construction of cer-
tain new forms of thermo-baro-
meters, 1 ; on a new instrument for
the mechanical trisection of an
angle ; and on the multisection of
an angle, 261.
Telegraphic cables, on the deposit of
submarine, 345.
Thermo-barometers, on the constnic-
tion of certain new forms of, 1.
Thermophyllite, on the doubly re-
fractive character of, 330.
Thiobenzoic acid, on the preparation
and constitution of, 283.
Thomson (Prof. J.) on some proper-
ties of ice at or near its meltmg-
point, 391.
Toynbee (J.) on the mode of trans-
mission of sonorous undulations in
the human ear, 5().
Troost (M.) on the specific gravities
of certain vapours at high tempera-
tures, 207.
Tuson (R. V.) on a carbonate of lead
from leaden coftins, 291.
Tyndall (Dr.) on the transmission of
radiant heatthrough gaseous bodies,
60 ; on the infiuence of magnetic
force on the electric di.scharge, 2.39.
Ufer (M.) on the nitride of chromium,
27s.
Uloth (M.) on ericinone, 51.
Urea, on the occurrence of, in the
organs of the Plagiostomons fislies,
79.
Vapour densities, on certain, 207.
Veatch (Dr. J. A.) on the occurrence
of boracic acid in the sea -water of
the Pacific, 323.
Voltaic batteries, on the use of in-
soluble com|)ouuds in, 404 ; on the
use of sulphate of lead in, 469.
Vowel sounds, on, 8l.
476
I N D E X.
Yulpic aoiil, on the prepnration nml
constitution of, 21 1 .
Ward (F. O.) on the pseiulo-diascopc,
79.
Water from the coal-strata, on the
composition of, 3'M.
Waterstou (J. J.) on the heat en-
gendered by the possible fall of a
meteor into the sun, 33S.
Wiedemann (G) on the oonductibility
of certain alloys for heat and elec-
tricity, 243.
Wood (S. v., jun.) on the probable
events which succeeded the close of
the Cretaceous neriod, 319.
Woods (Dr. T.) on a new actinometer,
Woolhouse ^W. S. B.) on tlio deposit
of submarine cables, 345.
Wright (Dr. S.) on the behaviour of
mercury as an electrode, 129.
Wright (Dr. "I on the lower lias of the
south of England, 400.
Wurtz CSl.) on new derivatives of gly-
col, 123 ; on a series of new bases,
125.
Xanthine, on the occurrence of. in
muscle and in the pancreas, 213.
END OF THE NINETEENTH VOLLME.
PRINTED BY TAYLOR AND FRANCIS,
RED LION COURT, FLEET STREET.
fr\ PLAMM.\M.
7
QC
1
P4
V.I9
Physical &
Applied Sci,
Serials
The Philosophical magazine
PLEASE DO NOT REMOVE
CARDS OR SLIPS FROM THIS POCKET
UNIVERSITY OF TORONTO LIBRARY
C 1C-.C
^
IL^
txC *
-ff^Cf
iJE-^
^^v*^
^; *s'
" <-^^' ■
"'' f '
fp
^'^'^
c '•-
\ 9^^^'
f^ i
', C'i
> ^p^ -'■ - t-
%'^- ■■ ■■
^t
h^< *
£t
'OCC:
'c.' C ^' "
^■^v
^&^
i- y-ri-
'^i ^'i
<^^^
-^f %l
g^C
\^ T*
-, Ct'
C<^'^V 4
B
U
< :>
Live Music Archive
Librivox Free Audio
Metropolitan Museum
Cleveland Museum of Art
Internet Arcade
Console Living Room
Books to Borrow
Open Library
TV News
Understanding 9/11